Jiu Liu

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.

The existence of a ground-state solution for a class of Kirchhoff-type equations in ℝ N

In this paper, we study the following Kirchhoff-type equation: where a , b are positive constants and N = 1, 2, 3. Under appropriate assumptions on V , K and g , we obtain a ground-state solution by using the approach developed by Szulkin and Weth in 2010.

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 .

A ground state solution for an asymptotically periodic quasilinear Schrödinger equation

Abstract This article is concerned with the existence of positive ground state solutions for an asymptotically periodic quasilinear Schrodinger equation. By using a change of variables, the quasilinear problem is transformed into a semilinear one. Then, we use a Nehari-type constraint to get the existence result.