一类具衰减位势的Schrdinger-Poisson方程变号基态解的存在性

Existence of Least Energy Sign-changing Solutions for Class of Schrdinger-Poisson Equation with Potential Vanishing at Infinity

本文研究一类具有衰减位势的Schrdinger-Poisson方程变号基态解的存在性,应用Nehari流形和变分方法,我们得到了该类方程存在一个变号基态解.进一步,如果该问题具有对称性时,我们证明了无穷多个非平凡解的存在性.在本文的结论中非线性项只要求是连续的.

In this paper, we study a class of Schrodinger-Poisson equation with potential vanishing at infinity. Using Nehari manifold and variational methods, we find a least sign- changing solution to this problem. Morover, if the problem presents symmetry, we prove the existence of infinitely many nontrivial solutions. In our results the nonlinearity is only required to be continuous.