Jia-Feng Liao

A uniqueness result for Kirchhoff type problems with singularity

Abstract In this work, by using the minimax method and some analysis techniques, we obtain the uniqueness of positive solutions for a class of Kirchhoff type problems with singularity.

A positive ground state solution for a class of asymptotically periodic Schrödinger equations

In this paper, by using the reformative conditions, a class of asymptotically periodic Schrodinger equations are studied. Via the variational method, a positive ground state solution is obtained.

A positive ground state solution for a class of asymptotically periodic Schrödinger equations with critical exponent

Abstract In the paper, by using a new condition, a class of asymptotically periodic Schrodinger equations with critical exponent are studied. Via the variational method, a positive ground state solution is obtained.

The Brezis-Nirenberg result for the Kirchhoff-type equation in dimension four

Abstract In this article, we study the Brezis-Nirenberg result for Kirchhoff-type equation in dimension four. Using the variational method, the existence of positive solutions and the multiplicity of solutions are obtained. It is worth to point out that a global Palais-Smale compactness condition for the critical problem is obtained. Thanks to this global Palais-Smale compactness condition, k pairs of distinct solutions are obtained, where .