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

Article type: Research Article

Authors: Liang, Shuaishuai | Shi, Shaoyun^{; *}

Affiliations: School of Mathematics, Jilin University, Changchun 130022, Jilin, P.R. China

Correspondence: [*] Corresponding author. E-mail: shisy@mail.jlu.edu.cn.

Abstract: In this paper, we study a class of the (p,q) Kirchhoff type problems with convolution term in RN. 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.

Keywords: Double phase Kirchhoff problems, potential well, multi-bump solutions, convolution term, variational methods

DOI: 10.3233/ASY-231827

Journal: Asymptotic Analysis, vol. 134, no. 1-2, pp. 85-126, 2023