一类相对非线性薛定谔方程解的存在性

Existence of Nontrivial Solutions for a Class of Relativistic Nonlinear Schrodinger Equations

利用临界点理论考虑了一类相对非线性薛定谔方程,主要通过变量代换将相对非线性薛定谔方程转化成半线性椭圆型方程.首先考虑位势函数为零时,将经典的场方程结果推广到了相对非线性薛定谔方程;而后利用临界点理论得到了有界位势情形方程非平凡解的存在性,在此情形,改进了文献[12-13]中的超线性条件.

Using the critical point theory, we consider a class of relativistic nonlinear Schrodinger equations. By introducing a change, we transform the relativistic nonlinear Schrodinger equations into the semilinear elliptic equations. First, we extend results of the classical field equation to the relativistic nonlinear Schrodinger equation. Then, the variational methods was used to obtain the existence of nontrivial solutions of the relativistic nonlinear Schrodinger equations with bounded potential. Moreover, we improved the general superlinear conditions which was used in [12-13].