Affiliation:
1. College of Science, Heilongjiang Institute of Technology, Harbin 150050, China
2. No. 703 Research Institute, China State Shipbuilding Co., Ltd., Harbin 150078, China
Abstract
In this article, we are interested in the study of the following Kirchhoff–Choquard equations: −a+b∫R2|∇u|2dxΔu+V(x)u=λ(ln|x|∗u2)u+f(u),x∈R2, where λ>0,a>0,b>0, V and f are continuous functions with some appropriate assumptions. We prove that when the parameter λ is sufficiently small, the above problem has a mountain pass solution, a least energy solution and a ground state solution by applying the variational methods and building some subtle inequalities.
Funder
Heilongjiang Institute of Technology Doctoral Research Start-up Fund
Heilongjiang Higher Education Teaching Reform Research Project
Heilongjiang Institute of Technology Education and Teaching Reform Research Project
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)