Multiple solutions of the Kirchhoff-type problem in RN

Abstract

In this paper, we concern with a class of quasilinear Kirchhoff-type problem. By using the Ekeland’s Variational Principle and Mountain Pass Theorem, the existence of multiple solutions is obtained. Besides, we also take this problem as an example to give the main frame of using critical point theory to find the weak solutions of nonlinear partial differential equation.

Keywords

• mountain pass theorem
• ekeland’s variational principle
• kirchhoff-type problem
• (ps) sequence
• 35j62
• 58k05
• 58e05