曲阜师范大学学报（自然科学版）2020，Vol.46Issue(3)：9-17,9.DOI:10.3969/j.issn.1001-5337.2020.3.009
二非线性椭圆方程的非平凡无穷多解
Infinitely many solutions for two nonlinear elliptic equations
摘要
Abstract
The following nonlinear elliptic equations{-Δu+λu=μ|u|q-2u+f(x,u),u ∈ H10(Ω),λ>-λ1,(Q1) is studied.For λ≤-λ1 ,a more general elliptic equation (P1):{-Δu+λu=f(x,u),u∈H10(Ω),λ≤-λ1(P1) will be taken into consideration.Ω??N is a bounded domain with smooth boundary;μ>0 is a parameter andλ1 is the first eigenvalue of -Δ in H10(Ω),1<q <2,f ∈C (-Ω×?,?).Due to lacking the (AR)condition and λ≤-λ1 in (P1 ),we can't use the Mountain pass theorem to handle the problems in chapter two.We will first show that (P1 )admits nontrivial solutions by using Local linking theorem under the (C )* condition. Then by applying the Fountain theorem under the (Cerami)condition to the elliptic equation (Q1 )with con-cave-convex nonlinear terms,the existence of infinitely many solutions is proved.关键词
非线性椭圆方程/凹凸非线性/喷泉定理/局部环绕定理/(C)*条件/(Cerami)条件Key words
nonlinear elliptic equation/noncave and convex terms/Fountain theorem/Local linking theorem/(Cerami)condition/(C )* condition分类
数理科学引用本文复制引用
鲁一宪,钱爱侠..二非线性椭圆方程的非平凡无穷多解[J].曲阜师范大学学报（自然科学版）,2020,46(3):9-17,9.基金项目
Chinese National Science Foundation(11571197). （11571197）
