一类非线性方程非平凡解的存在性

Existence of Nontrivial Solutions for a Class of Nonlinear Equations

本文通过变量代换,将非线性问题转换为半线性问题,把原来在Orlicz空间讨论的问题,放到Sobolev空间中进行讨论,并通过改进的AR条件,运用山路引理,证明了此问题存在非平凡解.

In this paper,the nonlinear problem is transformed into a semilinear problem by a variable transformation,and the original problem discussed in Orlicz space is put into in Sobolev space for discussion.Through the improved AR condition and the application of Mountain Pass Lemma,it is proved that there is a nontrivial solution to this problem.