Existence, concentration and multiplicity of solutions for (p,N)-Laplacian equations with convolution term

Abstract

In this paper, we concern some qualitative properties of the following [Formula: see text]-Laplacian equations with convolution term: [Formula: see text] where [Formula: see text] is a positive parameter, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] satisfies the critical exponential growth. By using the variational methods and the penalization method, we prove the existence of solutions for the above equations which concentrates at a local minimum of [Formula: see text] in the semi-classical limit as [Formula: see text]. Moreover, we obtain the multiplicity of solutions for the above equations by the Morse theory.