一类非局部问题的多解性

On Multiplicity of Solutions for a Class of Nonlocal Problem

研究了如下一类非局部问题:{-((a-b∫Ω|▽u|~2dx)Δu=λu^p x∈Ωu=0 x∈Ω其中Ω■RN(N≥3)是一个非空有界区域,a,b,λ>0,0<p<1为参量.利用山路引理,获得了该问题的2个非平凡解.

The following nonlocal problem is considered：{-（（a-b∫Ω｜▽u｜^2dx）Δu=λu^p x∈Ωu=0 x∈Ω where Ω■RN（N≥3）is a smooth bounded domain,a,b,λ0,0p1are parameters.By the Mountain Pass Lemma,the existence of two nontrivial solutions is obtained.