Quasilinear elliptic problems with exponential growth via the Nehari manifold method: Existence of nonnegative and nodal solutions

作     者：Giovany FIGUEIREDO Sandra Moreira Ricardo Ruviaro 

作者机构：Address Departamento de Matematica Universidade de Brasilia Departamento de Matematica e InformaticaUniversidade Estadual do Maranhao Departamento de Matematica Universidade de Brasilia 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))

年 卷 期：2024年

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

摘      要：In this paper we will be concerned with the problem -Δu-1/2Δ(a（x）u2)u+V（x）u=f（u）,x∈R2，where V is a potential continuous and f : R → R is a superlinear continuous function with exponential subcritical or exponential critical growth. We use as a main tool the Nehari manifold method in order to show existence of nonnegative solutions and existence of nodal solutions. Our results complement the classical result of solutions for quasilinear Schrodinger equations via the Nehari method due to Jia-quan Liu, Ya-qi Wang and Zhi-Qiang Wang in the sense that in this article we are considering nonlinearity of the exponential type.