Existence and Multiplicity Results for a Class of Nonlinear Schrödinger Equations with Magnetic Potential Involving Sign-Changing Nonlinearity
Year: 2022
Author: Francisco Odair de Paiva, Sandra Machado de Souza Lima, Olimpio Hiroshi Miyagaki
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 2 : pp. 148–177
Abstract
In this work we consider the following class of elliptic problems $\begin{cases} −∆_Au + u = a(x)|u|^{q−2}u + b(x)|u|^{p−2}u & {\rm in} & \mathbb{R}^N, \\u ∈ H^1_A (\mathbb{R}^N), \tag{P} \end{cases}$ with $2 < q < p < 2^∗ = \frac{2N}{N−2},$ $a(x)$ and $b(x)$ are functions that can change sign and satisfy some additional conditions; $u \in H^1_A (\mathbb{R}^N)$ and $A : \mathbb{R}^N → \mathbb{R}^N$ is a magnetic potential. Also 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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2021-0001
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 2 : pp. 148–177
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Magnetic potential sign-changing weight functions Nehari manifold Fibering map.