一类带扰动的非线性椭圆型方程组无穷多弱解的存在性(英文)  

On the Existence of Infinitely Many Solutions for Some Nonlinear Elliptic Systems with Perturbations

作　　者：胡业新[1] 

机构地区：[1]上海财经大学应用数学系,上海200433

出　　处：《应用数学》2007年第4期681-687,共7页Mathematica Applicata

基　　金：Supported by NSFC (10271077);the foundation for improvements of science research of the Shanghai University of finance and economics(211-8-5)

摘　　要：本文在一定条件讨论了如下一类带扰动项,且被两个Laplacian算子控制的非线性椭圆方程Dirichlet问题无穷多弱解的存在性.-Δu=|u|α-1|v|β+1u+f,x∈Ω,-Δv=|u|α+1|v|β-1v+g,x∈Ω,u(x)=v(x)=0,x∈Ω,其中-Δu∶=-div(u),(u,v)∈E∶=H01(Ω)×H10(Ω),(f,g)属于E的对偶空间.In this paper,we study the existence of infinitely many solutions for a class of non-linear elliptic systems governed by two Laplacian operators involving perturbations under some conditions.（-△u=∣u∣α-1∣υ∣β＋1u＋f,x∈Ω,-△υ=∣u∣α＋1∣υ∣β-1υ＋g,x∈Ω,u（x）＋ υ（x）=0,x∈（e）Ω,）where-△u：=-div（▽u）,（u,υ）∈E：=H10（Ω）× H10（Ω）,（f,g）∈E^＊.

关 键 词：临界点 (PS)条件 扰动方法 

分 类 号：O175.25[理学—数学]