带有扰动项的Henon方程的多解性研究

Multiple Solutions for the Nonlinear Henon Equation Under Perturbations

研究了下面带有非齐次扰动项的Henon方程其中B是全空间R^N,N>4上的单位球.应用Bahri-Berestycki(见文献[3])中的扰动方法,证明了对任意的h(x)=h(y,z)=h(|y|,|z|)∈L^2(B),x=(y,z)∈R^1×R^(N-1),当α>N+2时,存在常数p_(N,l)>2使得对任意的p∈(2,p_(N,l)),方程(P)存在无穷多互异解.

In this paper,we are concerned with the following nonlinear elliptic problemHereΩ（？）R～N,N 〉 4 is smooth and bounded.Applying the perturbation method introducedby Bahari-Berestycki,for any h（x） = h（y,z） = h（／y／,／z／）∈L～2（Ω）,x =（y,z）∈R_l×R～（N-l）,whenα〉 N ＋ 2,we show that there exists p n,l 〉 2 such that for any p∈（2,pN,l）,problem（P） has infinity many distinct solutions.