An Elliptic Equation Involving Exponential Critical Growth in ℝ2-Reference-Cited by-同舟云学术

An Elliptic Equation Involving Exponential Critical Growth in ℝ2

Published:2015-02-01 Issue:1 Volume:15 Page:23-37
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Albuquerque Francisco S. B.¹,Medeiros Everaldo S.²

Affiliation:

1. Centro de Ciências Exatas e Sociais Aplicadas Universidade Estadual da Paraíba, 58700-070, Patos-PB, Brazil

2. Departamento de Matemática Universidade Federal da Paraíba, 58051-900, João Pessoa-PB, Brazil

Abstract

Abstract We study the following class of nonhomogeneous Schrödinger equations −Δu + V(|x|)u = Q(|x|) f(u) + h(x) in ℝ2, where V and Q are unbounded or decaying radial potentials, the nonlinearity f (s) has exponential critical growth and the nonhomogeneous term h belongs to the dual of an appropriate functional space. By combining minimax methods and a version of the Trudinger-Moser inequality, we establish the existence and multiplicity of weak solutions for this class of equations.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2015-0102/pdf

Reference13 articles.

1. On the variational principle;Ekeland;Math Anal Appl,1974

2. do de A nonhomogeneous elliptic problem involving critical growth in dimension two;Medeiros;Math Anal Appl,2008

3. A sharp form of an inequality by Indiana;Moser;Math J,1971

4. The concentration - compactness principle in the calculus of variations Part Iberoamericana;Lions;Rev Mat,1985

5. Existence of solitary waves in higher dimensions An elliptic equation involving exponential critical growth in Nonlinear Schro dinger equations with unbounded and decaying radial potentials;Strauss;Math Phys Contemp Math,1977

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity;Electronic Journal of Differential Equations;2024-02-05

2. On a nonhomogeneous Kirchhoff type elliptic system with the singular Trudinger-Moser growth;Discrete and Continuous Dynamical Systems;2022

3. Standing wave solutions for a class of nonhomogeneous systems in dimension two;Complex Variables and Elliptic Equations;2016-03-08