一类退缩的拟线性椭圆方程正解的多重性

Multiplicity of Positive Solutions for a Class of Degenerated Quasilinear Elliptic Equations

讨论一类退缩的拟线性椭圆方程在有界域Ω RN上的 Dirichlet问题 :(P) - . (g(| u|α) | u|α- 2 u) =λ(x) um +uq,u≥ 0 ,u 0 ,inΩ ,u| Ω =0 ,至少有两个正解的存在性 ,其中 2 <2α <N ,0 <m <1,2α <q <q*- 1,q*=2αNN - 2α.

We obtain at least two positive solutions for the following problems(P): -·(g(｜u｜ α)｜u｜ α-2 u)=λ(x)u m+u q,u≥0,u0,in Ω, u｜ Ω=0, whereΩR N is a bounded domain with smooth boundary Ω,2<2α<N,0<m<1,2α<q<q *-1 and q *=2αNN-2α.