Existence and Multiplicity Results for a Class of Nonlinear Schrödinger Equations with Magnetic Potential Involving Sign-Changing Nonlinearity

作     者：Francisco Odair de Paiva Sandra Machado de Souza Lima Olimpio Hiroshi Miyagaki Francisco Odair de Paiva;Sandra Machado de Souza Lima;Olimpio Hiroshi Miyagaki

作者机构：Departamento de MatematicaUFSCarSao CarlosSP13560-970 Brazil Departamento de Ciencias ExatasBiologicas e da TerraINFES-UFFSanto Antonio de Padua-RJ28470-000Brazil 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2022年第38卷第2期

页      面：148-177页

核心收录：

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

基　　金：grants from FAPESP 2017/16108-6 grants from FAPESP 2019/24901-3 and CNPq 307061/2018-3 supported by CAPES/Brazil and the paper was completed while the second author was visiting the Departament of Mathematics of UFJF whose hospitality she gratefully acknowledges 

主　　题：Magnetic potential sign-changing weight functions Nehari manifold Fibering map 

摘      要：In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2qp2^(∗)=2N/N−2,a(x)and b(x)are functions that can change sign and satisfy some additional conditions;u∈H_(A)^(1)(R^(N))and A:R^(N)→R^(N) is a magnetic *** using the Nehari method in combination with other complementary arguments,we discuss the existence of infinitely many solutions to the problem in question,varying the assumptions about the weight functions.