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

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.