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arXiv · 1304.4767

Multiple solutions for a NLS equation with critical growth and magnetic field

Claudianor O. Alves·Giovany M. Figueiredo
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Abstract

In this paper, we are concerned with the multiplicity of nontrivial solutions for the following class of complex problems $$ (-i\nabla - A(\mu x))^{2}u= \mu |u|^{q-2}u + |u|^{2^{*}-2}u \ \mbox{in} \ \Omega, \ \ \ \ u \in H^{1}_{0}(\Omega,\mathbb{C}), $$ where $\Omega \subset \mathbb{R}^{N} (N \geq 4)$ is a bounded domain with smooth boundary. Using the Lusternik-Schnirelman theory, we relate the number of solutions with the topology of $\Omega$.

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Claudianor O. Alves, Giovany M. Figueiredo. 2013-04-17. Multiple solutions for a NLS equation with critical growth and magnetic field. https://arxiv.org/abs/1304.4767

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