Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 47, pp. 1-16.

Title: Existence of at least four solutions for Schrodinger equations with magnetic
potential involving and sign-changing weight function
       
Authors: Francisco Odair de Paiva (Univ. Federal de Sao Carlos, Brazil)
         Sandra Machado de Souza Lima (INFES-UFF, Santo Antonio de Padua, RJ, Brazil)
         Olimpio Hiroshi Miyagaki (Univ. Federal de Sao Carlos, Brazil)

Abstract:
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.

Submitted January 13, 2022. Published July 11, 2023.
Math Subject Classifications: 35J20, 35Q60, 35Q55, 35B38.
Key Words: Magnetic potential; Nehari method; sign-changing function; variational method.