Existence and multiplicity of multi-bump solutions for the double phase Kirchhoff problems with convolution term in R N

Abstract

In this paper, we study a class of the ( p , q ) Kirchhoff type problems with convolution term in R N . With the appropriate assumptions on potential function V and convolution term f, together with the penalization techniques, Morse iterative method and variational method, the existence and multiplicity of multi-bump solutions are obtained for this problem. In some sense, our results also generalize some known results.