Francisco Odair de Paiva, Sandra Machado de Souza Lima, Olimpio Hiroshi Miyagaki
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.
DOI: https://doi.org/10.58997/ejde.2023.47
Show me the PDF file (387 KB), TEX file for this article.
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Francisco Odair de Paiva Departamento de Matemática Universidade Federal de São Carlos (UFSCar) São Carlos - SP, CEP 13565-905, Brazil email: odair@dm.ufscar.br |
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Sandra Machado de Souza Lima Departamento de Ciências Exatas, Biológicas e da Terra INFES-UFF, Santo Antônio de Pádua - RJ, Brazil email: sandra.msouzalima@gmail.com |
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Ol&icute;mpio Hiroshi Miyagaki Departamento de Matemática Universidade Federal de São Carlos (UFSCar) São Carlos - SP, CEP 13565-905, Brazil email: olimpio@ufscar.br |
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