Study On The Existence Of Solutions For Two Classes Of Elliptic Equations On Unbounded Domains

In this paper,the existence of solutions of two classes of elliptic equations(systems)on unbounded domains is studied mainly by using the variational method,mountain pass lemma,Hardy inequality,even functional critical point theorem and the principle of centrality compactness,the main work is to overcome the difficulty of lacking of compactness.First,we study the existence of solutions for a class of semilinear elliptic equations with weight functions in unbounded domains where Ω is the outer domain with smooth boundary in RN(N≥3);0?Ω;2<p<2*;μ>0;2*=2N/(N-2).Secondly,we study the existence of solutions for a class of elliptic systems with Hardy term in unbounded domains where Ω is the unbounded domain with smooth boundary in RN(N≥3);0∈Ω;λ>0;α,β>1;2<α+β<2*;2*=2N/(N-2).