Positive solutions for double singularly perturbed Schroedinger Maxwell systems
Marco Ghimenti, Anna Maria Micheletti
TL;DR
This paper investigates the existence and number of positive solutions for a double singularly perturbed Schrödinger-Maxwell system, linking solutions to the topological complexity of the domain using Lusternik-Schnirelmann theory.
Contribution
It establishes a new connection between the number of solutions and the topological properties of the domain for the Schrödinger-Maxwell system.
Findings
Number of solutions depends on the domain's topology.
Non-contractible domains yield at least cat(A)+1 solutions.
Lusternik-Schnirelmann category theory is used to derive results.
Abstract
We show that the number of solutions of a double singularly perturbed Schroedinger Maxwell system on a smooth bounded domain A depends on the topological properties of the domain. In particular if A is non contractible we obtain cat(A) + 1 positive solutions. The result is obtained via Lusternik Schnirelmann category theory
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Differential Equations and Numerical Methods