Article
Mathematics, Applied
Van Duong Dinh
Summary: We revisit the finite time blow-up problem for the fourth-order Schrodinger equation with a specific nonlinearity, proving the existence of non-radial blow-up solutions with negative energy using localized virial estimates and spatial decay of the nonlinearity. This result is the first one dealing with non-radial blow-up solutions to the fourth-order Schrodinger equations.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics
Jichao Wang, Ting Yu
Summary: In this paper, we study the singular perturbation problem for the Schrodinger-Poisson equation with critical growth. We establish the relationship between the number of solutions and the profiles of the coefficients when the perturbed coefficient is small. Additionally, we observe a different concentration phenomenon without any restriction on the perturbed coefficient and obtain an existence result.
Article
Mathematics, Applied
Chenglin Wang, Jian Zhang
Summary: In this paper, the nonlinear Schrodinger equation with a partial confinement is studied using cross-constrained variational arguments and invariant manifolds of the evolution flow, leading to the derivation of sharp conditions for global existence and blowup of the solution.
MATHEMATICAL CONTROL AND RELATED FIELDS
(2022)
Article
Mathematics, Applied
Jingjing Pan, Jian Zhang
Summary: This paper investigates the mass-critical variable coefficient nonlinear Schrodinger equation, and explores the existence, compactness, and uniqueness of the ground state solutions.
ADVANCES IN NONLINEAR ANALYSIS
(2022)
Article
Mathematical & Computational Biology
Min Gong, Hui Jian, Meixia Cai
Summary: In this article, the global existence and stability issues of the nonlinear Schrödinger equation with partial confinement are considered. By establishing new cross-invariant manifolds and variational problems, a new sharp criterion for global existence is derived in different cases. The existence of orbitally stable standing waves is then obtained using the profile decomposition technique. This work extends and complements previous results.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics
Hideo Takaoka
Summary: The study focused on the Cauchy problem of the mass critical nonlinear Schrodinger equation with derivative and a mass of 4 pi. Global well-posedness was proven in H-1 under certain conditions, and the limiting profile of blow up solutions with the critical 4 pi mass was obtained using the concentration compact principle as originally done by Kenig-Merle.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Evelyn Richman, Christof Sparber
Summary: This study examines the strong magnetic field limit of a nonlinear Iwatsuka-type model, demonstrating that the equation can be effectively described by a nonlocal nonlinear model using a high-frequency averaging technique. It is also shown that in this asymptotic regime, inhomogeneous nonlinearities are confined along the y-axis.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Ruobing Bai, Bing Li
Summary: In this work, the concentration phenomenon of an inhomogeneous nonlinear Schrodinger equation was studied. It was proven that the solution blows up in finite time under certain conditions. These results are the first of their kind for the case when the initial data does not have finite variance and is non-radial. Furthermore, the first result for the infinite time blow-up rate was obtained.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2023)
Article
Mathematics, Applied
Van Duong Dinh
Summary: This paper investigates the Cauchy problem for nonlinear Schrodinger equations as an effective model of the Bose-Einstein condensate in a magnetic trap rotating with an angular velocity. The study establishes sufficient conditions for the existence of global-in-time and finite time blow-up solutions, derives sharp thresholds for global existence versus finite time blow-up in different mass cases, and examines the existence and strong instability of ground state standing waves. Finally, the paper proves the existence, non-existence, and orbital stability of prescribed mass standing waves when the rotational speed is smaller than a critical value.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Quanqing Li, Jian Zhang, Jianjun Nie, Wenbo Wang
Summary: This paper focuses on a generalized quasilinear Schrodinger equation with a nonlocal term. By using variational methods and category theory, the existence and multiplicity of semiclassical solutions for this problem are established.
ANALYSIS AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Li Wang, Jun Wang, Qiaocheng Zhong, Kun Cheng
Summary: This paper focuses on a fractional relativistic Schrödinger-Choquard equation with critical growth, which includes a fractional relativistic Schrödinger operator, a continuous potential, and a super-linear continuous nonlinearity. Under suitable assumptions, a family of positive solutions with exponential decay is constructed, which concentrate around a local minimum of the potential as ε approaches zero.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2023)
Article
Engineering, Mechanical
William Anderson, Mohammad Farazmand
Summary: This study investigates the reduced-order modeling of nonlinear dispersive waves described by nonlinear Schrodinger (NLS) equations. Two nonlinear reduced-order modeling methods are compared: the reduced Lagrangian approach based on the variational formulation of NLS, and the recently developed method of reduced-order nonlinear solutions (RONS). The surprising result is that, despite their apparent differences, these two methods can be obtained from the real and imaginary parts of a single complex-valued master equation. The study also reveals that the reduced Lagrangian method fails to predict the correct group velocity of waves in the NLS equation, while RONS accurately predicts the correct group velocity.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Van Duong Dinh, Sahbi Keraani
Summary: In this study, a scattering criterion and a blow-up criterion for nonradial solutions to the focusing inhomogeneous nonlinear Schrodinger equation were established using concentration/compactness and rigidity methods. The research also included an examination of long time dynamics of nonradial solutions with different initial data conditions, as well as the existence of finite time blow-up solutions with cylindrically symmetric data. The robust ideas developed in this paper can be applied to other types of nonlinear Schrodinger equations.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2021)
Article
Mathematics
Chao Ji, Neng Su
Summary: In this paper, the existence and stability of standing waves for the mixed dispersion nonlinear Schrodinger equation with a partial confinement in L-2-subcritical and L-2-supercritical cases are studied. The spectral theory of the equation is also proven, which serves as a useful tool in dealing with the problems at hand. The profile decomposition and concentration-compactness principle play a critical role in the presented proofs.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Materials Science, Multidisciplinary
Stephanie Ganyou, Serge I. Fewo, Cherif S. Panguetna, Timoleon C. Kofane
Summary: The dynamics of (2+1)-dimensional ion-acoustic wave packets in magnetized electroneg-ative plasma are studied. The obtained nonlinear Schrodinger equation depends on system parameters and the magnetic field. The modulational instability and the characteristics of the ion-acoustic waves are analyzed using the variational method.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)