Article
Mathematics, Applied
Ziheng Zhang, Ying Wang, Rong Yuan
Summary: This article studies the nonlinear Schrodinger-Poisson system with pure power nonlinearities, and shows the existence of a ground state sign-changing solution with precisely two nodal domains, by using constraint variational method and a variant of the classical deformation lemma. This improves and generalizes the existing results by Wang, Zhang, and Guan.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2021)
Article
Mathematics
Ying Wang, Ziheng Zhang
Summary: This article investigates the Kirchhoff-Schrodinger-Poisson system with pure power nonlinearity, and finds a ground state solution for the problem under proper assumptions on the potentials V, K, and h with the help of Nehari manifold.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2021)
Article
Mathematics, Applied
Hui Jian, Shenghao Feng, Li Wang
Summary: In this paper, we study a Kirchhoff-Schrodinger-Poisson system with logarithmic and critical nonlinearity. By combining the constraint variational method and perturbation method, we prove the existence of a least energy sign-changing solution with two nodal domains. Furthermore, we show that the energy of this solution is strictly larger than twice the ground state energy.
Article
Mathematics, Applied
Xiaotao Qian
Summary: This paper investigates a nonlocal problem and proves the existence of a ground state sign-changing solution with energy strictly larger than the ground state energy. The asymptotic behavior of the solution as the parameter approaches zero is also discussed.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Shenghao Feng, Jianhua Chen, Jijiang Sun, Xianjiu Huang
Summary: In this paper, the existence of least energy sign-changing solutions for the Kirchhoff-Schrödinger-Poisson equation is considered. The paper proves that the least energy sign-changing solutions are strictly larger than the ground state energy and analyzes the concentration phenomenon of these solutions as certain parameters tend to infinity or zero.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2023)
Article
Mathematics, Applied
Ting Xiao, Yaolan Tang, Qiongfen Zhang
Summary: This paper deals with a Kirchhoff-type equation and proves the existence of at least one sign-changing solution by considering a minimization problem on a special constraint set. The results, especially when p is within the range of (1, 3), can be considered as an improvement on existing findings.
Article
Mathematics, Applied
Mengyu Wang, Xinmin Qu, Huiqin Lu
Summary: This paper investigates the existence of least energy sign-changing solutions for nonlinear elliptic equations driven by nonlocal integro-differential operators with critical nonlinearity. Through constrained minimization method and topological degree theory, the paper obtains a least energy sign-changing solution under weaker conditions, and also establishes an existence theorem for sign-changing solutions of fractional Laplacian equations with critical growth.
Article
Mathematics, Applied
Ziheng Zhang, Ying Wang
Summary: This article focuses on the existence and characterization of solutions for the Schrodinger-Poisson system. It investigates the existence of a positive ground state solution and a sign-changing solution with precisely two nodal domains. The study utilizes the Nehari manifold and Hofer's deformation lemma, and establishes the existence and regularity of the solutions through variational methods and interior Lp estimates. Moreover, it proves that the energy of the sign-changing solution is strictly larger than that of the ground state solution.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Xiao-Ping Chen, Chun-Lei Tang
Summary: This paper investigates a critical Schrodinger-Poisson system and obtains a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains by using variational methods with a more general global compactness lemma. It is also proved that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, the paper further analyzes the exponential decay of the positive least energy solution and can be regarded as the supplementary work of a previous study.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Ren-Ting Feng, Chun-Lei Tang
Summary: This paper investigates a class of nonlinear Kirchhoff equations and proves the existence and energy relationship of sign-changing ground state solutions using the Nehari manifold, while also obtaining the convergence property of solutions. The weaker hypotheses presented in this article contribute to advancing the field compared to previous work.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Anmin Mao, Shuai Mo
Summary: This article studies the nonlocal Schrodinger problem with general nonlinearities and the semiclassical ground state solutions of Nehari-Pohoaey type. By making assumptions on the potential V, improved existence results are obtained, along with the analysis of the concentration behavior of the ground state solutions in the limit case. These results extend previous related research.
ADVANCES IN NONLINEAR ANALYSIS
(2022)
Article
Mathematics, Applied
Qing Yang, Chuanzhi Bai
Summary: In this paper, we investigate a fractional Kirchhoff type problem and prove the existence of sign-changing ground state solutions using constraint variational method and analysis techniques.
Article
Mathematics, Applied
Jiabin Zuo, Khaled Khachnaoui, J. Vanterler da C. Sousa
Summary: In this paper, the author investigates the existence of ground state solutions for an electromagnetic Schrodinger equation in exterior domains. The main technical approach involves the joint use of the Nehari manifold method, variational methods, and topological methods.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Fei-Fei Liang, Xing-Ping Wu, Chun-Lei Tang
Summary: In this paper, the authors investigate the existence of non-trivial ground state solution in the coupled nonlinear Schrodinger-Korteweg-de Vries system with periodic potential using the variational method and Nehari manifold.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Fuyi Li, Cui Zhang, Zhanping Liang
Summary: In this paper, the existence of ground-state solutions for the nonlinear Schrodinger-type equation in the presence of a magnetic field is established using variational methods. The equation is considered under suitable assumptions and for sufficiently small values of the parameter λ.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(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)