带类p(x)-拉普拉斯算子的问题在全空间上的多重解

Infinitely Many Solutions Involving p(x)-Laplacian-like Operator

研究了全空间中一类带类p(x)-拉普拉斯算子的问题.在非线性项不满足(AR)条件时,通过证明该类问题的泛函满足Cerami条件,利用对称山路引理和变分方法,获得了该类问题无穷多解的存在性.

In this paper,a class of problems have been studied with p(x)-Laplacian-like operator in R.Under the condition that the Nonlinear term does not satisfy the(AR) condition,it has been proved that the functional of such problems satisfies Cerami condition,and the existence of infinitely many solutions via the symmetric mountain pass lemma and the variational method has been proved.