一类带有梯度的p(x)-Laplace方程正解的存在性

Positive solutions for a class of p(x)-Laplace problems involving gradient term

本文讨论如下p(x)-Laplace方程边值问题正解的存在和不存在性:-△_(p(x))u+g(u)■▽u■^(p(x))=λu^(q(x))x∈Ω,u=0x∈Ω,(1),其中Ω是R^N中有界开子集,p(x)∈C(Ω),q(x)∈C(Ω),N≥1,p(x)>1,q(x)>1,g:[0,∞)→[0,∞)的非负连续函数.λ是给定的常数.

In this thesis, we discuss the followingp（x）-Laplace Dirichlet problem {-△p（x）u＋g（u）｜△↓｜^p（x）=λu^q（x） x∈Ω, x∈δΩ, where Ω is a bounded open subset of R^Np（x）∈C（Ω^-）,q（x）∈C（Ω^-）,N≥1,p（x）〉1,q（x）〉1,g：[0,∞）→[0,∞）is anonnegative continuous ftmction. λ is a given constant.