Article
Mathematics, Applied
Dumitru Baleanu, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran
Summary: This article focuses on the existence and stability results of mild solutions for random impulsive stochastic integro-differential equations with noncompact semigroups and resolvent operators in Hilbert spaces. The authors use Hausdorff measures of noncompactness and the Mo spacing diaeresis nch fixed point theorem to prove the existence of mild solutions. They also investigate stability results, including continuous dependence of initial conditions, Hyers-Ulam stability, and mean-square stability of the system, by developing new analysis techniques and establishing an improved inequality.
Article
Mathematics
Yunfeng Li, Pei Cheng, Zheng Wu
Summary: This paper focuses on the problem of pth moment and almost sure exponential stability of impulsive neutral stochastic functional differential equations (INSFDEs). Two sufficient criteria for the exponential stability of INSFDEs are derived based on Lyapunov function and average dwell time (ADT), which are more convenient to be used than the Razumikhin conditions in previous literature.
Article
Computer Science, Artificial Intelligence
Zhiyong Huang, Chunliu Zhu, Jinwu Gao
Summary: This paper introduces the Lyapunov's second method for studying stability of uncertain differential equations, presenting two sufficient conditions and validating the theoretical findings through illustrative examples.
FUZZY OPTIMIZATION AND DECISION MAKING
(2021)
Article
Mathematics, Applied
Ravikumar Kasinathan, Ramkumar Kasinathan, Varshini Sandrasekaran, Juan J. Nieto
Summary: In this paper, the existence and stability of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups in Hilbert spaces are investigated using resolvent operators. The existence of mild solution is proved by utilizing Monch fixed point theorem and considering the Hausdorff measures of noncompactness. The stability results include continuous dependence of solutions on initial conditions, exponential stability, and Hyers-Ulam stability for the aforementioned system. An example is provided to demonstrate the obtained results.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics
Dongwen Zhang, Qi Liu, John Michael Rassias, Yongjin Li
Summary: We investigate the Hyers-Ulam stability of an equation involving a single variable and propose a new method that does not require any restrictions on the parity, domain, and range of the function. Stability theorems are proven using this method for various functional equations involving several variables. Our findings suggest that this method is easy and appropriate for investigating the stability of functional equations, particularly for several variables.
Article
Mathematics, Applied
Jianxin He, Fanchao Kong, Juan J. Nieto, Hongjun Qiu
Summary: This paper studies a kind of delayed impulsive neutral differential equations (DINDEs) and establishes conditions for the existence, uniqueness, and global exponential stability of the solutions using contraction mapping principle and inequality technology.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Engineering, Multidisciplinary
N. Senu, K. C. Lee, A. Ahmadian, S. N. I. Ibrahim
Summary: This paper develops a numerical approach based on the two-derivative Runge-Kutta type method for solving a special type of third-order delay differential equations with constant delay. The proposed method, named TDRKT3(5), utilizes Newton interpolation and demonstrates high efficiency and validity in solving third-order pantograph type delay differential equations. The stability analysis of the TDRKT3(5) method is also investigated. Numerical experiments confirm the effectiveness of the new method and suggest the possibility of extending it to solve fractional and singularly perturbed delay differential equations.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Electrical & Electronic
Milad Zarif Mansour, Si Phu Me, Sajjad Hadavi, Babak Badrzadeh, Alireza Karimi, Behrooz Bahrani
Summary: In this article, the transient stability conditions for a grid-following voltage-source converter (VSC) are found using Lyapunov's stability theorem. A new stability analysis method and system strength index are proposed. The correctness of the proposed method is validated through simulation and experiment.
IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS
(2022)
Article
Automation & Control Systems
Yahao Chen, Stephan Trenn
Summary: This paper investigates the solutions and stability properties of switched nonlinear differential-algebraic equations (DAEs). It introduces a novel concept of solutions, called impulse-free (jump-flow) solutions, and provides a geometric characterization that establishes their existence and uniqueness. The stability conditions based on common Lyapunov functions are effectively applied to switched nonlinear DAEs with high-index models, and the commutativity stability conditions are extended from switched nonlinear ordinary differential equations to switched nonlinear DAEs. Simulation results involving switching electrical circuits are presented to demonstrate the practical utility of the developed stability criteria in analyzing and understanding the behavior of switched nonlinear DAEs.
Article
Mathematics
Mingli Xia, Linna Liu, Jianyin Fang, Yicheng Zhang
Summary: This paper studies the asymptotic stability problem for a class of stochastic differential equations with impulsive effects. We derive a sufficient criterion on asymptotic stability using Lyapunov stability theory, bounded difference condition and martingale convergence theorem. The results indicate that impulses can enhance the stability of the stochastic differential equations when the original system is unstable. Finally, we validate the feasibility of our results through two numerical examples and simulations.
Article
Mathematics, Interdisciplinary Applications
Guangjie Li, Qigui Yang
Summary: This paper investigates the exponential stability of the theta-method for neutral stochastic functional differential equations with Markovian switching and jumps. It is shown that the trivial solution is almost surely and mean-square exponentially stable, and the same conclusion holds for the theta-method. Numerical examples are provided to illustrate the obtained results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Interdisciplinary Applications
Sandip Maji, Srinivasan Natesan
Summary: This article discusses an efficient numerical method for solving nonlinear time-fractional integro-partial differential initial-boundary-value problems. The non-linearity is tackled using the Newton linearization process. The non-symmetric interior penalty Galerkin method is applied for the spatial variable, and a semi-discrete problem is obtained in the time variable. By using L1-scheme and L2-scheme for the time-fractional derivative, and trapezoidal rule for the integral term, a fully-discrete scheme is derived.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Min Li, Chengming Huang, Ziheng Chen
Summary: In this paper, a compensated projected Euler-Maruyama method for stochastic differential equations with jumps is presented and analyzed. The method achieves mean square convergence under a coupled condition and allows for superlinear jump and diffusion coefficients. New techniques are developed for convergence analysis due to the different moment properties of Poisson and Brownian increments. Numerical experiments confirm the theoretical results.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Rizwan Rizwan, Akbar Zada, Manzoor Ahmad, Syed Omar Shah, Hira Waheed
Summary: This paper considers a switched coupled system of nonlinear implicit impulsive Langevin equations with mixed derivatives. The existence, uniqueness, and generalized Ulam-Hyers-Rassias stability of the proposed model are observed under certain conditions using the Generalized Diaz-Margolis's fixed point approach on a generalized complete metric space. An example is provided to support the main result.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Lijiao Wu, Haixiang Zhang, Xuehua Yang
Summary: This paper presents an efficient numerical method for fourth-order partial integro-differential equations with weakly singular kernel. The method is constructed on graded meshes and achieves second-order convergence for weakly singular solutions. Numerical results demonstrate its effectiveness, and further improvement in convergence order is achieved using the extrapolation method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
A. O. Ignatyev
APPLIED MATHEMATICS LETTERS
(2018)
Article
Mathematics, Applied
Alexander O. Ignatyev
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2011)
Article
Mathematics, Applied
Alexander O. Ignatyev, Oleksiy A. Ignatyev
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2011)
Article
Mathematics
A. O. Ignatyev
MATHEMATICAL NOTES
(2020)
Article
Mathematics
A. O. Ignatyev
LOBACHEVSKII JOURNAL OF MATHEMATICS
(2017)
Article
Mathematics, Applied
Alexander O. Ignatyev, Oleksiy Ignatyev
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
(2011)
Article
Mathematics, Applied
AO Ignatyev, OA Ignatyev
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2006)
Article
Mathematics, Applied
SR Bernfeld, C Corduneanu, AO Ignatyev
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2003)
Article
Mathematics, Applied
IV Barteneva, A Cabada, AO Ignatyev
APPLIED MATHEMATICS AND COMPUTATION
(2003)
Article
Mathematics, Applied
AO Ignatyev
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2002)
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)