On coupled nonlocal Schrödinger–Kirchhoff system with singular exponential nonlinearity in $\mathbb{R}^N$

Abstract

This paper is concerned with the existence of solutions for parameters dependent Schrödinger–Kirchhoff system driven by nonlocal integro-differential operators with singular Trudinger–Moser nonlinearity in the whole Euclidean space $\mathbb{R}^N$. These parameters have a major impact on the produced analysis. It is noted that, we also study the asymptotic behaviour of solutions depending upon these parameters. The proofs of the existence results to the aforementioned system rely on the mountain pass theorem, the Ekeland variational principle, the classical deformation lemma, and the Krasnoselskii genus theory. The salient feature and novelty of this paper is that it also covers the so-called degenerate case of the Kirchhoff function, that is, it could vanish at zero.

Keywords

• nonlocal integro-differential operator
• mountain pass theorem
• variational principle
• genus theory