Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces

TL;DR

This paper investigates the existence and multiplicity of solutions to magnetic Kirchhoff equations within Orlicz-Sobolev spaces, employing critical point theory and various conditions to establish multiple solution results.

Contribution

It introduces new existence and multiplicity results for Kirchhoff equations in magnetic fractional Orlicz-Sobolev spaces, including ground-state solutions and solutions under weak conditions.

Findings

Existence of non-trivial solutions under Ambrosetti-Rabinowitz condition

Existence of ground-state solutions

Unbounded sequence of solutions

Abstract

In this paper, we study the existence and multiplicity of weak solutions to a general type of Kirchhoff equations in magnetic fractional Orlicz-Sobolev spaces. Specifically, we appeal to Critical Point Theory to prove the existence of non-trivial solutions under the so-called Ambrosetti-Rabinowitz condition. We also state the existence of ground-state solutions. Moreover, multiplicity results which yield the existence of an unbounded sequence of solutions are also provided. Finally, we show existence under a weak-type Ambrosetti-Rabinowitz condition formulated in the framework of Orlicz spaces.