Existence at least four solutions for a Schr\"odinger equation with magnetic potential involving sign-changing weight function

In this paper we consider the following class of elliptic problems $$- \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,$$ for $x \in \mathbb{R}^N$, $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_{\lambda}(x)$ is a sign-changing weight function, $b_{\mu}(x)$ has some aditional con...

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Bibliographic Details
Main Authors de Paiva, Francisco Odair Vieira, Lima, Sandra Machado de Souza, Miyagaki, Olimpio Hiroshi
Format Journal Article
LanguageEnglish
Published 12.04.2019
Subjects
Mathematics - Analysis of PDEs
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Summary:In this paper we consider the following class of elliptic problems $$- \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,$$ for $x \in \mathbb{R}^N$, $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_{\lambda}(x)$ is a sign-changing weight function, $b_{\mu}(x)$ has some aditional conditions, $u \in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow\mathbb{R}^N$ is a magnetic potential. Exploring the Bahri Li argument and some preliminar results we will discuss the existence of four solution to the problem in question.
DOI:10.48550/arxiv.1904.06336