含参数拟线性非齐次椭圆型方程的多重解

Multiple Solutions for Quasilinear Nonhomogeneous Elliptic Equations with a Parameter

该文研究如下形式的拟线性非齐次椭圆型方程-△_pu-△_p(|u|^(2α))|u|^(2α-2)u+V(x)|u|^(p-2)u=h(u)+g(x), x∈R^N,其中1 <p≤N (N≥3),1/2 <α≤1,V∈C(R^N,R), h∈C(R,R),而且扰动项g∈L^p'(R^N),这里p'=p/(p-1).利用变量代换结合极小极大方法可以证明该问题存在多重解.

In this paper, we study the following quasilinear nonhomogeneous elliptic equations of the form -△pu-△p(|u|^2α)|u|^2α-2u+V(x)|u|^p-2u=h(u)+g(x), x∈R^N, where 1<p≤N(N≥3), 1/2<α≤1, V∈C(RN,R), h∈C(R,R) and g∈L^p′(R^N), where p′=p/p-1, is a disturbance term. Using a variable replacement and minimax method, we show the existence and multiplicity of solutions to this problem.