Existence of at least four solutions for Schrodinger equations with magnetic potential involving and sign-changing weight function

Electronic Journal of Differential Equations

article

Francisco Odair de Paiva¹  Sandra Machado de Souza Lima²  OlImpio Hiroshi Miyagaki¹ 

[1] Departamento de Matemática Universidade Federal de São Carlos;Departamento de Ciências Exatas

关键词: Magnetic potential;    Nehari method;    sign-changing function;    variational method.;   

DOI  :  10.58997/ejde.2023.47

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

We consider the elliptic problem $$- \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u , $$ for \(x \in \mathbb{R}^N\), \( 1 < q < 2 < p < 2^*= 2N/(N-2)\),\(a_{\lambda}(x)\) is asign-changing weight function, \(b_{\mu}(x)\) satisfies some additional conditions,\(u \in H^1_A(\mathbb{R}^N)\) and \(A:\mathbb{R}^N \to \mathbb{R}^N\) is a magneticpotential. Exploring the Bahri-Li argument and some preliminary results we willdiscuss the existence of a four nontrivial solutions to the problem in question.

【 授权许可】

CC BY