一类非局部近共振问题多重解的存在性

Existence of Multiple Solutions for a Class of Nonlocal Near Resonance Problems

通过变分方法在光滑有界域Ω上研究由常数a,b>0,参数λ>0及连续函数f(x,u)共同决定的非局部问题:{-(a-b integral from Ω|▽u|~2dx)Δu+bλu^3=f(x,u)x∈Ω u=0 x∈Ω利用Ekeland变分原理和山路引理得到该问题近共振情形多重解的存在性.

In this paper,we use the variational method to study the following nonlocal problems in the smooth bounded domain Ω,which are determined by the constant a,b0,the parameter λ0 and the continuous function f（x,u）：{-（a-b integral from Ω｜▽u｜~2 dx）Δu＋bλu^3=f（x,u） x ∈ Ω u=0 x ∈Ω The existence and multiple solutions are obtained for this class of problems with near resonance by the Ekeland variational principle and a mountain pass lemma.