Article
Mathematics, Applied
Kun Cheng, Li Wang
Summary: This paper studies the Kirchhoff-Schro spacing diaeresis dinger-Poisson system, and establishes the existence of solutions with a prescribed number of nodes using various theoretical methods. The paper also analyzes the energy of the solutions as the number of nodes changes.
Article
Mathematics, Applied
Marcelo F. Furtado, Ying Wang, Ziheng Zhang
Summary: This article considers the Schrodinger-Poisson system and establishes the existence of positive ground state solutions and ground state nodal solutions using the constraint minimization argument.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics
Xing Wang, Rui He, Xiangqing Liu
Summary: In this paper, the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth is studied. Through the perturbation method, a sequence of localized nodal solutions is established near a given local minimum point of the potential function. New analytical skills are employed to overcome the obstacles caused by the nonlocal term. The results improve and extend related ones in the literature.
ACTA MATHEMATICA SCIENTIA
(2022)
Article
Mathematics, Applied
Zhen-Li Yang, Zeng-Qi Ou
Summary: In this paper, the existence of nodal solutions for a class of Schrödinger-Poisson systems is studied. The proof relies on constrained variational method and quantitative deformation lemma, showing the existence of a nodal solution with positive energy for lambda values satisfying certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
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
Yao Du, Jiabao Su, Cong Wang
Summary: This paper establishes the existence of nontrivial solutions for a Schrödinger-Poisson system by variational methods, which is a new system coupled by Schrödinger equation of p-Laplacian with a Poisson equation. Techniques are applied to ensure the boundedness of the Palais-Smale sequence.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Xueqi Sun, Yueqiang Song
Summary: The paper investigates the existence of least-energy nodal solutions for a critical Schrodinger-Poisson system on the Heisenberg group. It discusses the properties of the solutions and the challenges faced in the study.
ANALYSIS AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Chao Wang, Juntao Sun
Summary: This paper investigates normalized solutions to the planar Schrodinger-Poisson systems with square-root nonlinearity, and proves the existence of normalized solutions by establishing a new estimate on the square-root nonlinearity.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Xilin Dou, Xiaoming He
Summary: This paper investigates a class of fractional Schrodinger-Poisson systems with a critical nonlocal term and multiple competing potentials. By using mathematical methods, it is proved that a positive ground state solution exists under appropriate assumptions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Juntao Sun, Tsung-fang Wu
Summary: This paper investigates the multiplicity of two spike nodal solutions for a nonautonomous Schrodinger-Poisson system in R-3 with a specific nonlinearity. It is concluded that under certain assumptions, the system admits multiple distinct nodal solutions, each with two nodal domains. The proof is based on a natural constraint approach and the generalized barycenter map.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Xueqin Peng, Gao Jia, Chen Huang
Summary: This paper investigates the Schrodinger-Poisson system with critical exponent, showing the existence of infinitely many solutions with negative energy under suitable conditions, and the existence of infinitely many solutions with positive energy. The main tools used are the concentration compactness principle, Z(2) index theory, and Fountain Theorem. These results extend some existing results in the literature.
Article
Mathematics, Applied
Yao Du, Jiabao Su, Cong Wang
Summary: In this paper, by applying scaling transformations and ingenious methods, the bounded Palais-Smale sequences are produced, and the existence of nontrivial solutions for a quasilinear elliptic system coupled by a Schrodinger equation with p-Laplacian operator and a Poisson equation is obtained through the mountain pass theorem.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Hui Guo, Ronghua Tang, Tao Wang
Summary: This paper utilizes Miranda's theorem and deformation lemma along with new analytic techniques to prove the existence of radial nodal solutions with prescribed number of nodal domains for the Schrodinger-Poisson system.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Xiaoping Wang, Fangfang Liao, Fulai Chen
Summary: In this paper, the planar Schrodinger-Poisson system is considered and converted to an integro-differential equation with logarithmic convolution potential. The existence of an axially symmetric mountain-pass type solution is proven using new estimates on logarithmic convolution potential. These results improve upon previous research by Chen and Tang (2020) and others.
APPLIED MATHEMATICS LETTERS
(2024)
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
Claudianor O. Alves
Summary: In this paper, an abstract theorem is presented that can be used to prove the existence of solutions for a class of elliptic equations and related problems. Furthermore, it is shown using this abstract theorem that a class of zero mass problems has multiple solutions, which is a novelty for this type of problem.
MILAN JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Claudianor O. Alves, Angelo R. F. de Holanda
Summary: In this work, we study the existence of nontrivial solutions for a class of semilinear degenerate elliptic equations. We overcome the difficulties involving the Grushin operator by proving some crucial compactness results. For the case of a = 1, we show a Berestycki-Lions type result.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
(2023)
Article
Mathematics, Applied
Ricardo L. Alves, Claudianor O. Alves
Summary: In this paper, we study the existence and concentration of solutions for a class of quasilinear problems. When (h) over bar 0 is sufficiently small, we prove the existence and concentration of solutions. The solutions are characterized by v as a mapping function, W as a C-1 singular functional satisfying technical conditions, and V as a continuous function with specific limit properties. Furthermore, we also analyze the existence of solutions for all (h) over bar > 0 when V is a radial function.
ANNALI DI MATEMATICA PURA ED APPLICATA
(2023)
Article
Mathematics
Claudianor Oliveira Alves, Liejun Shen
Summary: This paper studies the planar Schrodinger equations with Stein-Weiss convolution parts. By establishing a general version of Poho.zaev identity and using a general minimax principle, the existence of mountain-pass type solutions for the equation is investigated. It is shown that, despite the absence of monotonicity restriction on the nonlinearity f, the mountain-pass value equals the least energy level. This study extends previous research results to lower dimensions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Claudianor O. O. Alves, Romildo N. N. de Lima, Alannio B. Nobrega
Summary: This paper studies the existence and non-existence of solutions for the Ambrosetti-Prodi type problem {-delta u = P(x) (g(u) + f (x)) in R-N, u E D-1,D-2(R-N), lim(|x|->+infinity) u(x) = 0, where N >= 3, P is an element of C(R-N, R+), f is an element of C (R-N) & cap; L-infinity (R-N), and g is an element of C-1 (R). The main tools used are the sub-super-solution method and Leray-Schauder topological degree theory.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Claudianor O. O. Alves, Tahir Boudjeriou
Summary: The goal of this paper is to demonstrate the existence of a bounded variation solution by using the Anzellotti pairing in an evolution problem associated with the minimal surface equations. The key step in the proof is to approximate the parabolic minimal surface problem with a quasilinear parabolic problem involving a parameter p > 1. By establishing energy estimates independent of p, the limit as p -> 1(+) is taken to obtain the desired result.
ANALYSIS AND MATHEMATICAL PHYSICS
(2023)
Article
Mathematics
Claudianor O. Alves, Giovanni Molica Bisci, Luca Vilasi
Summary: We prove a local minimum result for a one-parameter family of C(1) functionals on Finsler manifolds and derive several theoretical consequences. We finally apply our abstract result to obtain the existence of solutions for some classes of nonlinear constrained problems, including equations on compact Riemannian manifolds without boundary, and Neumann problems governed by the p-Laplacian operator.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics
J. Abrantes Santos, C. O. Alves, J. Zhou
Summary: This work studies the existence of positive solutions for a class of semipositone quasilinear problems in a bounded domain O. The main tools used are variational methods, a concentration compactness theorem for Orlicz-Sobolev space, and some priori estimates.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics, Applied
Claudianor O. Alves, Luciano M. Barros, Cesar E. Torres Ledesma
Summary: In this paper, we study the existence of a solution for a class of variational inequality in whole RN with critical growth nonlinearity for N ≥ 2. By combining penalization schemes from del Pino and Felmer (Calc Var 4:121-137, 1996) and Bensoussan and Lions (Applications des inequations variationelles en controle stochastique. Dunod, Paris, 1978), we improve upon a recent result by Alves et al. (J Math Anal Appl 494:124672, 2021).
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Claudianor O. Alves, Ismael S. da Silva
Summary: This paper concerns the existence of multiple solutions for a Schrodinger logarithmic equation. The multiplicity of solutions is established by using the notion of Lusternik-Schnirelmann category and introducing a new function space.
ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Claudianor O. Alves, Eduardo de S. Boer, Olimpio H. Miyagaki
Summary: In this work, we investigate the existence of normalized solutions to the Schroedinger-Poisson system with a nonlinearity f exhibiting exponential critical growth. The main results of this study extend and/or complement previous findings in [3] and [13].
DIFFERENTIAL AND INTEGRAL EQUATIONS
(2023)
Article
Mathematics
Claudianor O. Alves, Chao Ji
Summary: In this paper, the existence and multiplicity of multi-peak positive solutions for the logarithmic Schrodinger equation are shown using variational methods. The equation is -ε^2△u + V(x)u = ulogu^2, in R-N, with u in H-1(R-N), where c > 0, N = 2, and V: R-N -> R is a multi-well potential.
ISRAEL JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Claudianor O. Alves, Renan J. S. Isneri
Summary: In this paper, variational methods are used to establish the existence of a heteroclinic solution for the prescribed mean curvature equation of a specific form. The equation involves a double-well potential function, and certain conditions are imposed on the parameters for the existence of the solution.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Claudianor O. Alves, Chao Ji
Summary: In this paper, the existence and concentration of solitary waves for a class of generalized Kadomtsev-Petviashvili equations with potential in R2 are studied using variational methods.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Claudianor Oliveira Alves, Angelo Roncalli Furtado de Holanda
Summary: In this work, we study the existence of solutions for a class of semilinear degenerate elliptic equations in the whole space R2, which involve the Grushin operator and a nonlinearity that has critical growth and exponential growth. By combining various mathematical tools and methods, we prove the existence of at least one nontrivial weak solution.
MATHEMATISCHE NACHRICHTEN
(2023)
