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
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
Zhiying Cui, Wei Shuai
Summary: We investigate the existence of sign-changing solutions for a Kirchhoff-type equation with a double integral term and a Laplace operator term. The boundary condition is zero. By imposing restrictions on the parameters a, b, λ and the potential function h, we prove the existence of sign-changing solutions and analyze their asymptotic behavior as b approaches zero or infinity. Furthermore, if the positive part of the potential function contains several disjoint components, we also demonstrate the existence of multi-bump sign-changing solutions.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics, Applied
Lifeng Yin, Wenbin Gan, Shuai Jiang
Summary: This article considers the existence of a class of Kirchhoff-type equations and describes the concentration of ground state solutions as the parameter varies.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Cui Zhang, Fuyi Li
Summary: This paper investigates the existence and properties of solutions for a class of Schrodinger equations using Nehari manifold and constrained minimization arguments, and it also studies the asymptotic behavior of the solutions.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
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, Applied
Nazli Irkil, Erhan Piskin, Praveen Agarwal
Summary: This work focuses on a system of Kirchhoff-type equations with viscoelastic term and logarithmic nonlinearity. The global existence was proven by combining potential well method with Faedo-Galerkin's procedure, followed by establishing decay rate estimates using multiplier method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Jie Yang, Haibo Chen, Senli Liu
Summary: The aim of this paper is to study the existence and multiplicity of nonnegative solutions for a critical Kirchhoff equation involving the fractional p-Laplace operator. By applying various mathematical methods, this study investigates the existence and multiplicity of nonnegative solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Xia Li, Wen Guan, Da-Bin Wang
Summary: We deal with sign-changing solutions for the Kirchhoff equation and prove the existence of at least one least energy sign-changing solution under certain conditions. The nonlinearity term lambda u + mu vertical bar u vertical bar(2)u fails to satisfy super-linear near zero and super-three-linear near infinity.
Article
Mathematics
Menghui Wu, Chunlei Tang
Summary: In this paper, the existence of ground state sign-changing solutions is studied for a nonlinear Kirchhoff type equation with a steep potential well. It is shown that when a certain parameter lambda is large enough, there exist sign-changing solutions with precisely two nodal domains, and their energy is strictly larger than twice that of the ground state solutions. The concentration phenomenon of these sign-changing solutions is also proven.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Mathematics, Applied
Yuan Gao, Yongsheng Jiang, Lishan Liu, Na Wei
Summary: In this paper, we investigate a logarithmic Kirchhoff type problem with variational methods and the maximum principle. Under certain assumptions on the potential function V(x), we prove that the problem has only trivial solution for large b > 0, and two positive solutions for small b > 0. Furthermore, we observe that the number of positive solutions is determined by the value of parameter b, considering both the local and nonlocal terms.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Yuanyuan Zhang, Yang Yang, Sihua Liang
Summary: This paper establishes sufficient conditions for the existence of least energy sign-changing weak solutions to a quasilinear nonhomogeneous N-Laplacian equation with logarithmic and exponential nonlinearities. The study considers both subcritical and critical exponential growths by using constrained minimization in the Nehari manifold.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Alok K. Sahoo, Bhakti B. Manna
Summary: In this paper, we consider the existence of nonradial sign-changing solutions for the Hamiltonian elliptic system in R-N. By working with the space of phi-equivariant functions, we establish our result in two different ways based on the size of the fixed point set.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(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
Shubin Yu, Ziheng Zhang
Summary: This paper investigates the existence of ground state sign-changing solutions in the Schrodinger-Poisson system, improving upon recent results by Khoutir (2021). Omega is a bounded smooth domain in R-3, with mu > 0 and lambda > 0.
APPLIED MATHEMATICS LETTERS
(2022)
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)
