一类p(x)-Laplace方程正解的存在性

Existence of positive solutions to a class of p(x)-Laplacian equations

考虑方程■正解的存在性,这里■是径向对称的,Ω=B(0,R)■RN是有界径向对称区域,其中R是充分大的正数．当 (?)时,证明了方程正解的存在性,而且未对f(0)的符号做任何限制．

We consider the equation {-△p（x）u=f（u）, x∈Ω, u=0, x∈δΩ,where -△p（x）u=-div （_△↓p（x）u=-div（｜△↓u^p（x）-2△↓u）, p（x）∈C^1 （R^N） is a radial function, Ω=B（0,R）belong to R^N is a bounded radial symmetric domain where R is big enough. We give the existence of positive solutions when lim u→＋∞ f（u）/ up^--1=0 In particular, we do not assume any sign condition on f（0）.