Existence Of Positive Solutions For Hardy Type Systems

In this paper, we discuss the existence of positive solutions of Hardy type systems in anbounded domain of RN, and the existence of the least energy solutions in a half space RN+. Thisthesis is divided into three chapters.In chapter1, we introduce the background and main results of the thesis. We illustratedifculties about the existence of the positive solutions for Hardy type systems.Chapter2is concerned with the existence of positive solutions of the following nonlinear ellipticsystems involving critical Hardy-Sobolev exponent where N≥4and is a C1bounded domain in RNwith0∈.0<s <2, α+β=2(s)=2(N s)N2,α, β>1, λ>0and1<p <N+2N2. The case when0belongs to the boundary of is closely relatedto the mean curvature at the origin on the boundary.We prove the existence of the least energysolutions of the following limiting problem: Since the best Hardy-Sobolev constant is achieved in RN+.Then we get the result.In chapter3, we investigate the existence of positive solutions to the system...