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

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 a sign-changing weight function, \(b_{\mu}(x)\) satisfies some additional conditions, \(u \in...

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Bibliographic Details
Published in:Electronic journal of differential equations 2023-07, Vol.2023 (1-??), p.47-16
Main Authors: De Paiva, Francisco Odair, Lima, Sandra Machado de Souza, Miyagaki, Olimpio Hiroshi
Format: Article
Language:English
Subjects:
magnetic potential
nehari method
sign-changing function
variational method
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Summary: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 a sign-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 magnetic potential. Exploring the Bahri-Li argument and some preliminary results we will discuss the existence of a four nontrivial solutions to the problem in question.
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2023.47