Article
Acoustics
Volodymyr Puzyrov, Jan Awrejcewicz, Nataliya Losyeva, Nina Savchenko
Summary: The article discusses the stability of a double pendulum under the influence of a follower force. The imperfect nature of the follower force is taken into account. The relationships between mass, stiffness, and damping coefficients are analyzed, and stability conditions are obtained. It is found that the critical load can be increased by adjusting the stiffness ratio.
JOURNAL OF SOUND AND VIBRATION
(2022)
Article
Acoustics
Haifa A. Alyousef, Alvaro H. Salas, Muteb R. Alharthi, Samir A. El-Tantawy
Summary: The forced damped parametric driven pendulum oscillators are analyzed using numerical and analytical methods. Different oscillators related to the problem are recovered and compared with Runge-Kutta numerical approximation.
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL
(2022)
Article
Mathematics, Applied
Hujun Yang, Xiaoling Han
Summary: This article investigates the forced pendulum equations of variable length x + kx' + a(t) sin x = e(t), where a(t) and e(t) are continuous T-periodic functions and k is a constant. Under suitable assumptions on a(t), e(t), and T, the existence of T-periodic solutions to the forced pendulum equations is proved using Mawhin's continuation theorem. Finally, specific examples and numerical simulations are given to illustrate the applicability of the conclusions in this paper.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mechanics
Ivan Polekhin
Summary: The paper investigates the planar inverted pendulum with a vibrating pivot point and an additional horizontal force field. The assumption is made that the pivot point oscillates rapidly in the vertical direction, commensurable with the period of the horizontal force. The research demonstrates the existence of asymptotically stable non-falling periodic solutions in the system, providing analytical and numerical results.
Article
Mathematics, Applied
Jurancy Ereu, Luz E. Marchan, Liliana Perez, Henry Rojas
Summary: In this paper, it is proven that a globally Lipschitz non-autonomous superposition operator satisfying certain conditions maps the space of functions of bounded second ?-variation into itself with its generator function satisfying a Matkowski condition. The existence and uniqueness of solutions for the Hammerstein and Volterra equations in this space are also established.
Article
Mathematics, Applied
J. Angel Cid
Summary: We present new sufficient conditions for the existence of T-periodic solutions for the phi-laplacian pendulum equation, utilizing a continuation theorem and enhancing or complementing previous results in the literature within the classical, relativistic, and curvature pendulum equations frameworks.
ADVANCES IN NONLINEAR ANALYSIS
(2021)
Review
Computer Science, Interdisciplinary Applications
Godiya Yakubu, Pawel Olejnik, Jan Awrejcewicz
Summary: This article presents a comprehensive review of variable-length pendulums, evaluating the current trends in the field through mathematical modeling, dynamical analysis, and computer simulations. The future perspectives and applications of variable-length pendulums are also discussed. The importance of basic knowledge of constant-length pendulums in accurately describing physical processes is emphasized. Additionally, an extended model for a variable-length pendulum's mechanical application is proposed, and its potential usage in reducing residual vibrations and applications in mechatronic and robotic systems are explored.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2022)
Article
Mathematics
Alvaro H. Salas, Ma'mon Abu Hammad, Badriah M. Alotaibi, Lamiaa S. El-Sherif, Samir A. El-Tantawy
Summary: This investigation presents analytical solutions for both conserved and non-conserved rotational pendulum systems, including exact and approximate solutions for the conserved oscillator, as well as analytical approximations for non-conserved oscillators. The comparison between exact and approximate solutions highlights the significance of these results for discussing and interpreting further research.
Article
Mathematics, Interdisciplinary Applications
Danfeng Luo, Mengquan Tian, Quanxin Zhu
Summary: This article investigates the finite-time stability of stochastic fractional-order delay differential equations. The equivalent form of the system is derived using Laplace transformation and inverse transformation. The uniqueness of the solution is proven by defining the maximum weighted norm in Banach space and using the principle of contraction mapping. Furthermore, the criteria for finite-time stability of the system with and without impulses are derived using HenryGronwall delay inequality and interval translation. Examples are provided to verify the correctness of the results.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Ivan Yu Polekhin
Summary: This paper investigates the global dynamics of the inverted spherical pendulum under the presence of a vertically rapidly vibrating suspension point and an external horizontal periodic force field. The authors prove the existence of a nonfalling periodic solution when the periods of the vertical motion and the horizontal force are commensurate. Numerical analysis further demonstrates the existence of an asymptotically stable nonfalling solution for a wide range of system parameters.
REGULAR & CHAOTIC DYNAMICS
(2022)
Article
Mathematics, Applied
Youness Chatibi, El Hassan El Kinani, Abdelaziz Ouhadan
Summary: This paper employs the Hydon method to determine discrete symmetries for a family of ordinary, partial, and fractional differential equations, and demonstrates how these symmetries can be used to construct new solutions from known ones.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Nazim Mahmudov, Arzu Ahmadova
Summary: This article deals with the well-posedness of an adapted solution to Caputo type fractional backward stochastic differential equations of order alpha is an element of (1/2, 1) whose coefficients satisfy a Lipschitz condition. A novelty of the article is the introduction of a new weighted norm in the square integrable measurable function space that is useful for proving a fundamental lemma and its well-posedness. For this class of systems, we then demonstrate the coincidence between the notion of stochastic Volterra integral equation and the mild solution.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Fahim Uddin, Faizan Adeel, Khalil Javed, Choonkil Park, Muhammad Arshad
Summary: In this article, the idea of double controlled M-metric space is introduced by using two control functions on the right-hand side of the triangle inequality. Examples of double controlled M-metric spaces are provided, along with fixed point results under new type of contractions in this setting. Furthermore, an example is presented to emphasize the importance of one of the main results.
Article
Mathematics, Interdisciplinary Applications
Leila Gholizadeh Zivlaei, Angelo B. B. Mingarelli
Summary: The article continues the development of the basic theory of generalized derivatives and provides applications, including necessary conditions for extrema, Rolle's theorem, the mean value theorem, the fundamental theorem of calculus, integration by parts, and an existence and uniqueness theorem for a generalized Riccati equation. It also proves that for each alpha > 1, there is a fractional derivative and a corresponding function whose fractional derivative fails to exist everywhere on the real line.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Jihua Yang
Summary: This paper studies the limit cycle bifurcations of a pendulum equation under non-smooth perturbations, obtaining upper bounds on the number of limit cycles in both oscillatory and rotary regions by expressing first order Melnikov functions as generating functions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Multidisciplinary Sciences
Pablo Amster, Pierluigi Benevieri, Julian Haddad
Summary: This research extends recent results for second-order ordinary equations with a superlinear term to delay equations, proving the existence of positive periodic solutions for nonlinear delay equations under certain superlinear growth and sign alternance conditions. The approach is topological and based on Mawhin's coincidence degree.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Mathematics
Pablo Amster
Summary: This paper provides an elementary proof of a Landesman-Lazer type result for systems using a shooting argument, and investigates its connection with the fundamental theorem of algebra.
MONATSHEFTE FUR MATHEMATIK
(2021)
Article
Mathematics
Pablo Amster
Summary: The elementary proof of the no-retraction theorem in the plane is provided using the complex square root method.
AMERICAN MATHEMATICAL MONTHLY
(2021)
Article
Mathematics, Applied
Pablo Amster, Melanie Bondorevsky
Summary: The study focuses on semi-dynamical systems associated with delay differential equations, providing criteria for weak and strong persistence, sufficient conditions for uniform persistence, and the existence of non-trivial T-periodic solutions. It is also shown that the conditions are necessary in some sense.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Mostafa Adimy, Pablo Amster, Julian Epstein
Summary: This paper investigates the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell population under external periodic regulatory factors. By using the method of characteristics to simplify the age-structured model to a nonautonomous system, the study proves the existence of periodic solutions under appropriate conditions using topological degree techniques and fixed point methods.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics
Pablo Amster, Julian Epstein, Arturo Sanjuan Cuellar
Summary: Motivated by results similar to those of Lazer-Leach, we investigate the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay. Our main technique will be the Coincidence Degree Theorem developed by Mawhin.
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS
(2021)
Article
Mathematics
P. Amster, J. Epstein
Summary: The abstract formulation of a duality principle established by Krasnoselskii is presented, showing that under appropriate conditions, finding fixed points of certain operators in different Banach spaces can lead to the solutions of a nonlinear functional equation sharing some topological properties. An explicit construction of such dual viewpoints is provided for a class of nonlinear functional equations, including both previously treated cases and novel ones.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Pablo Amster, Melanie Bondorevsky
Summary: This paper analyzes the N-dimensional generalization of Nicholson's equation, considering a model with multiple delays, nonlinear coefficients, and a nonlinear harvesting term. By deriving sufficient conditions from previous results, it guarantees strong and uniform persistence. Additionally, under suitable extra assumptions, the existence of T-periodic solutions is proven, and a convenient reversal of prior conditions demonstrates the zero as a global attractor.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Mathematics
P. Amster, J. Angel Cid
Summary: This study uses the complex square root to define a simple homotopic invariant and provides easy proofs of the plane Brouwer fixed point theorem and the Fundamental Theorem of Algebra.
EXPOSITIONES MATHEMATICAE
(2022)
Article
Mathematics
Pablo Amster
Summary: In a 1960 paper, Felix Browder established a theorem on the continuation of fixed points in a family of continuous functions. The theorem states that for a compact mapping in a convex, closed, and bounded subset of a normed space, the fixed points of the function family depend continuously on a parameter. The paper also discusses the applications of this theorem in nonlinear boundary value problems, presenting new perspectives, introducing novel results, and highlighting open problems.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Pablo Amster, Colin Rogers
Summary: This article introduces a prototype Ermakov-Painleve I equation and analyzes a homogeneous Dirichlet-type boundary value problem. In addition, a novel Ermakov-Painleve I system is established, which can be reduced to the autonomous Ermakov-Ray-Reid system through an involutory transformation, while augmented with a single component Ermakov-Painleve I equation. The Hamiltonian nature of such systems is limited.
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Pablo Amster, Gonzalo Robledo, Daniel Sepulveda
Summary: This article revisits and extends the results about the dynamics of a discrete and nonlinear matrix model describing the growth of a size-structured single microbial population in an autonomous chemostat to the nonautonomous framework. The first and second result determine the threshold for either the extinction or persistence of the total biomass. The main result establishes sufficient conditions for the existence, uniqueness, and global attractiveness of an omega-periodic solution.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Mathematics, Applied
Pablo Amster, Mariel Paula Kuna, Dionicio Santos
Summary: New results regarding the global stability, boundedness of solutions, and existence and non-existence of T-periodic solutions for a specific delayed equation involving a phi-Laplacian operator are obtained using a Lyapunov-Krasovskii functional. An application to the well-known sunflower equation is provided.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
(2022)
Article
Mathematics, Applied
Pablo Amster, Alberto Deboli, Manuel Pinto
Summary: The (omega, Q)-periodic problem for a system of delay differential equations is considered, with existence and multiplicity of solutions proven under different conditions. These conditions extend results for well-known periodic and anti-periodic cases. The results are particularly applicable to biological models with mixed terms and vectorial versions.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics, Applied
Pablo Amster, Mariel Paula Kuna, Dionicio Pastor Santos
OPUSCULA MATHEMATICA
(2020)
Article
Mathematics, Applied
Guglielmo Feltrin, Maurizio Garrione
Summary: This article deals with a non-autonomous parameter-dependent second-order differential equation driven by a Minkowski-curvature operator. It proves the existence of strictly increasing heteroclinic solutions and homoclinic solutions with a unique change of monotonicity under suitable assumptions, and analyzes the asymptotic behavior of these solutions.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Mehraj Ahmad Lone, Idrees Fayaz Harry
Summary: In this paper, we study Lorentzian generalized Sasakian space forms admitting Ricci soliton, conformal gradient Ricci soliton, and Ricci Yamabe soliton. We also investigate the conditions for solitons to be steady, shrinking, and expanding. Additionally, we provide applications of Ricci Yamabe solitons.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhihao Lu
Summary: We present a unified method for deriving differential Harnack inequalities for positive solutions to semilinear parabolic equations, subject to an integral curvature condition, on compact manifolds and complete Riemannian manifolds. In addition to the case of scalar equations, we also establish an elliptic estimate for the heat flow under the same condition, which is a novel result for both harmonic map and heat equations.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Giuseppe Cosma Brusca
Summary: We investigate the asymptotic behavior of the minimal heterogeneous d-capacity of a small set in a fixed bounded open set Omega. We prove that this capacity is related to the parameter lambda and behaves as C |log epsilon|^(1-d), where C is a constant.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Stefan Schiffer
Summary: This note investigates the complex constant rank condition for differential operators and its implications for coercive differential inequalities. Depending on the order of the operators, such inequalities can be viewed as generalizations of either Korn's inequality or Sobolev's inequality.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Konstantinos T. Gkikas, Phuoc-Tai Nguyen
Summary: This article studies the boundary value problem with an inverse-square potential and measure data. By analyzing the Green kernel and Martin kernel and using appropriate capacities, necessary and sufficient conditions for the existence of a solution are established in different cases.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Giovanni Bellettini, Simone Carano, Riccardo Scala
Summary: This article computes the relaxed Cartesian area in the strict BV-convergence for a class of piecewise Lipschitz maps from the plane to the plane, where the jump is composed of multiple curves that are allowed to meet at a finite number of junction points. It is shown that the domain of this relaxed area is strictly contained within the domain of the classical L1-relaxed area.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Federico Cacciafesta, Anne-Sophie de Suzzoni, Long Meng, Jeremy Sok
Summary: In this paper, we establish the well-posedness of a perturbed Dirac equation with a moving potential W satisfying the Klein-Gordon equation. This serves as a toy model for atoms with relativistic corrections, where the wave function of electrons interacts with an electric field generated by a nucleus with a given charge density. A key contribution of this paper is the development of a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation, which is of independent interest.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Jingwen Chen
Summary: In this article, the authors generalize their previous results to higher dimensions and prove the existence of eternal weak mean root 1 root-1 curvature flows connecting a Clifford hypersurface to the equatorial spheres.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Samuel Borza, Wilhelm Klingenberg
Summary: This article proves that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points, and characterizes conjugate points in ideal sub-Riemannian manifolds in terms of the metric structure of the space.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Christina Sormani, Wenchuan Tian, Changliang Wang
Summary: This article presents a sequence of warped product manifolds that satisfy certain hypotheses and proves that this sequence converges in a weak sense to a limit space with nonnegative scalar curvature.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Gianni Dal Maso, Davide Donati
Summary: In this paper, we study the F-limits of sequences of quadratic functionals and bounded linear functionals on the Sobolev space, and show that their limits can always be expressed as the sum of a quadratic functional, a linear functional, and a non-positive constant. Furthermore, we prove that the coefficients of the quadratic and linear parts in the Gamma-limit are independent of Omega, and introduce an example to demonstrate that the previous results cannot be generalized to every bounded open set.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Laura Abatangelo, Corentin Lena, Paolo Musolino
Summary: The paper provides a full series expansion of a generalization of the u-capacity related to the Dirichlet-Laplacian in dimension three and higher. The results extend the previous findings on the planar case and are applied to study the asymptotic behavior of perturbed eigenvalues when Dirichlet conditions are imposed on a small regular subset of the domain.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Gustavo de Paula Ramos
Summary: This paper employs the photography method to estimate the number of solutions to a nonlinear elliptic problem on a Riemannian orbifold, based on the Lusternik-Schnirelmann category of its submanifold of points with the largest local group.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Tim Espin, Aram Karakhanyan
Summary: This article discusses smooth solutions of the Monge-Ampere equation on an annular domain with two smooth, closed, strictly convex hypersurfaces as boundaries, subject to mixed boundary conditions. It is demonstrated that global C2 estimates cannot be obtained in general unless additional restrictions are imposed on the principal curvatures of the inner boundary and the Neumann condition itself, as shown by an explicit counterexample. Under these conditions, a priori C2 estimates are proven and it is shown that the problem has a smooth solution.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
