The Existence Of Solution For Semilinear Elliptic Equations

In this paper,we consider the existence of positive solutions for the following semelinear elliptic problemwhere N≥3, 2* = 2N/(N-2), 1<α< (N+2)/(N-2),μ∈(0,μ|-),μ|- = (N-2)²/4, k(x)∈C(R^N), D^1,2(R^N) defined as the completion of C₀^∞(R^N) with respect to the normIn this paper, we will use perturbation method to deal with this problem. Firstly, we will outline the abstract of this method, including percondition, basic idears and general steps. Then according to these, we study the problem and get the main result of this paper.The main result of this paper is:Theorem If k(x)∈C(R^N)∩L¹(R^N)∩L^∞(R^N), k(x) has constant sign ,and when |x|→∞, k(x)～x^β,β< (N-2)(α+1)/2-N, Then equation (1) possesses a solution as |ε| small enough.