摘要
在非线性项f满足适当的局部条件假设下,研究以下(2,p)-Laplace方程{-Δu-Δp u=f(u),x∈Ω,u=0,x∈δΩ,其中Ω■R^N是光滑的有界区域,2<p<N,f∈C(R,R).首先利用截断技术给出辅助方程;然后利用推广的Clark定理,证明了辅助方程有无穷多解;最后利用解的L^∞估计,证明所研究方程无穷多解的存在性.
Under appropriate local assumptions on the nonlinear term f,we consider the following(2,p)-Laplaceequation{-Δu-Δp u=f(u),x∈Ω,u=0,x∈δΩ,where Ω ■ R^Nis a bounded smooth domain 2<p<N,f∈C(R,R).Firstly,the auxiliary equation is given by truncation technique.Then the generalized Clark theorem is used to prove that the auxiliary equation has infinite solutions.Finally,using the L^∞ estimate of the solution,the existence of infinitely many solutions of the studied equationis proved.
作者
解利霞
梁占平
XIE Lixia;LIANG Zhanping(School of Mathematical Science,Shanxi University,Taiyuan 030006,China)
出处
《河南科学》
2019年第11期1721-1726,共6页
Henan Science
基金
国家自然科学基金（11571209）
