Existence and multiplicity results for a class of Kirchhoff-Choquard equations with a generalized sign-changing potential

Abstract

In the present work we are concerned with the following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})Δu +Q(x)u + μ(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M:\mathbb{R}\to \mathbb{R}$ given by $M(t)=a+bt$, $\mu >0$, $V$ a sign-changing and possible unbounded potential, $Q$ a continuous external potential and a nonlinearity $f$ with exponential critical growth. We prove existence and multiplicity of solutions in the nondegenerate case and guarantee the existence of solutions in the degenerate case.

22 pages

References in corpus (1)

• $(p,N)-$Choquard logarithmic equation involving a nonlinearity with exponential critical growth: existence and multiplicity