一类非局部椭圆算子的无穷多变号解

Infinitely Many Sign-Changing Solutions for Non-Local Elliptic Operators

本文的目的是研究如下非局部椭圆算子方程在Dirichlet边界条件下变号解的存在性{-L_ku=f(x,u)in Ω,u=0,in R^n\Ω,其中Ω∈R^n(n≥2)是具有光滑边界的有界区域,非线性项f满足超线性以及次临界增长条件.利用变号临界点定理,证明了在更弱的条件下无穷多变号解的存在性.

The purpose of this paper is to study the existence of sign-changing solu tions for the following equations driven by a non-local elliptic operator with homoge neous Dirichlet boundary conditions {-Lku=f（x,u）in Ω,u=0,in R^n／Ωhere Ω∈R^n（n≥2） is a boundary smooth domain, the nonlinear term f satisfies superlinear and subcritical growth conditions. By using a suitable sign-changing critical point, we obtain infinitely many sign-changing solutions under weaker conditions.