一类带权的非线性椭圆方程正解的存在性问题

Multiple Positive Solutions for a Class of Weighted Nonlinear Elliptic Equations

描述了一类带权的有狄立克莱边界条件的非线性椭圆方程:-div(|x|^(-2α)▽u)-μ/(|x|^(2(a+1)))u=|x|^(-bp)|u|^(p-2)u+λ|u|^(q-2)u在零点附近正解的存在性问题,其中0∈Ω是R^N(N≥3)中具有光滑边界的有界区域,并在临界的加权Sobolev-Hardy指数情况下得到两个正解.

Let 0∈Ω RN（N≥3） be a bounded domain with smooth boundary. We characterize an exact growth order near zero for positive solutions of a class of weighted nonlinear elliptic equations -div（｜x｜^-2a↓△u）u/｜x｜2（a＋1） u=｜x｜^-bp｜u｜^p-2u＋λ｜u｜^q-wu with Dirichlet boundary condition. Then we obtain multiple positive solutions for equations involving critical weighted Sobolev-Hardy exponents.