Article
Mathematics, Applied
Jing Zhang, Chao Ji
Summary: This paper focuses on a quasilinear Choquard equation and establishes the existence of ground state solutions using the variational method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Jie Yang, Hongxia Shi
Summary: In this article, the authors investigate a class of fractional Choquard equation with critical Sobolev exponent. They use a monotonicity technique and global compactness lemma to prove the existence of ground state solutions for this equation. Additionally, they also demonstrate the existence of ground state solutions for the corresponding limit problem.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Chun-Yu Lei, Binlin Zhang
Summary: This paper focuses on nonlinear Choquard equations with doubly critical growth, utilizing the Pohozaev-type identity to address compactness issues caused by doubly critical nonlinearities and establish the existence of a ground state solution.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Claudianor O. Alves, Giovany M. Figueiredo, Riccardo Molle
Summary: In this paper, the existence of positive solutions to an elliptic problem with parameter λ is proved under certain smallness assumptions on the parameters V-0 and λ, by applying variational methods combined with degree theory.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Xiaorong Luo, Anmin Mao
Summary: The existence of sign-changing solutions to the Choquard problem is proven by combining the Nehari manifold method with the Ljusternik-Schnirelman theory. The main results extend and complement earlier works.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics
Dongdong Qin, Vicentiu D. Radulescu, Xianhua Tang
Summary: This paper studies the non-autonomous Choquard-Pekar equation, under some general assumptions on the potential W and the nonlinearity f, ground state solutions are proved to exist. Infinitely many geometrically distinct solutions are also constructed using the variational method and deformation arguments.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Shuai Yuan, Sitong Chen
Summary: In this paper, we investigate the existence of ground state solutions for the fractional Choquard Logarithmic equation. Our paper extends and complements previous results by Boer and Miyagaki. We establish an energy inequality with a weaker assumption on f and use new variational and analytic techniques based on radial symmetry to obtain our final result.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics
J. I. A. N. W. E. I. Hao, J. I. N. R. O. N. G. Wang
Summary: This paper studies the Choquard equation with logarithmic nonlinearity and obtains a ground state solution under certain assumptions on V and H using variational method and logarithmic inequality. Additionally, the limit profiles of Choquard equations as alpha approaches 0 or N are investigated.
MISKOLC MATHEMATICAL NOTES
(2022)
Article
Mathematics, Applied
Jianfu Yang, Liping Zhu
Summary: This paper demonstrates the existence of at least cat(Ω)(Ω) positive solutions for the nonlocal equation under certain conditions, where lambda > lambda(0) and Ω is an unbounded domain with a bounded complement R-N\Ω.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Yuanyuan Luo, Dongmei Gao, Jun Wang
Summary: In this article, we study the Choquard equation and prove the existence of a ground state solution under certain conditions. We also provide some sufficient conditions for the existence and nonexistence of a ground state solution.
ACTA MATHEMATICA SCIENTIA
(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
Yong-Yong Li, Gui-Dong Li, Xing-Ping Wu
Summary: This paper investigates the non-autonomous Choquard equation and proves the existence and concentration of positive ground state solutions for lambda large enough.
APPLIED MATHEMATICS LETTERS
(2021)
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
Xiaoliang Xie, Tianfang Wang, Wen Zhang
Summary: (Summary in English:)
In this paper, we study the (p, q)-Laplacian equation with nonlocal Choquard reaction and obtain new existence results of nontrivial solutions under suitable conditions on the absorption potential and nonlinear term using variational methods.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics
Hui Guo, Tao Wang, Taishan Yi
Summary: This paper investigates the qualitative properties of positive ground state solutions to the nonlocal Choquard type equation on a ball BR. The radial symmetry of all positive ground state solutions is proven using Talenti's inequality. The Newton's Theorem is then developed and the uniqueness of the positive ground state solution is established using the contraction mapping principle. Finally, by constructing cut-off functions and applying energy comparison method, the convergence of the unique positive ground state solutions as the radius R tends to infinity is shown. These results extend and complement the existing literature.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Engineering, Multidisciplinary
Xiaoping Song, Dongliang Li, Maochun Zhu
Summary: This study investigates the properties of subcritical anisotropic Trudinger-Moser inequalities in Euclidean spaces and establishes a precise relationship between critical and subcritical inequalities. Additionally, critical anisotropic Trudinger-Moser inequalities are proven under nonhomogeneous norm restrictions, revealing a similar relationship with the supremums of subcritical inequalities.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
