MULTIPLE POSITIVE SOLUTIONS FOR KIRCHHOFF TYPE PROBLEMS INVOLVING CONCAVE AND CONVEX NONLINEARITIES IN R3

作者：Cao, Xiaofei; Xu, Junxiang^*; Wang, Jun

来源：Electronic Journal of Differential Equations, 2016, 301.

• Kirchhoff type problem
• Ekeland variational principle
• Nehari manifold

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theory of Lagrange multipliers.

• 出版日期2016-11-25
• 单位东南大学; 江苏大学