Positive Solutions For Neumann Boundary Value Problem Of Singular Elliptic Equations With Critical Expontents

In this paper, we consider the following semilinear elliptic equations with critical Sobolev exponents: By variational method,the existence of positive solution is obtained.First,we proof that the associated energy functional J(u) satisfy some geometry condition by Hardy inequality and promotion form,and get some results for J(u) by Mountain Pass Lemma without (PS) con-dition,that is,existing bounded sequence ut of H1(Ω), such that:J(ut)â†'C; J’(ut)â†'0,in H-1(Ω).Then,we show uk is bounded in H1(Ω),and uk is relatively compact in H1(Ω) by con-centration compactness theory and Sobolev inequality,and give result of existence of positive solution.Finally,we also consider the existence of positive solutions for the problem of the mixed boundary value and further research direction.