On existence and asymptotic behavior of solutions of elliptic equations with nearly critical exponent and singular coefficients

摘要

In this paper we study the existence and asymptotic behavior of solutions of?Δu=μu|x|2+|x|αup(α)?1?ε,u>0 in BR(0)with Dirichlet boundary condition. Here, ?2<α<0, p(α)=2(N+α)N?2, 0<ε(α)?1 and p(α)?1?ε is a nearly critical exponent. We combine variational arguments with the moving plane method to prove the existence of a positive radial solution. Moreover, the asymptotic behaviour of the solutions, as ε→0, is studied by using ODE techniques.