与广义p-Laplace算子相关的非线性边值问题在一族空间中解的存在性

The Existence of Solutions of Nonlinear Boundary Value Problems Involving the Generalized p-Laplacian Operator in a Family of Spaces

利用非线性增生映射值域的扰动定理,研究了非线性椭圆边值问题(1)在Ls(Ω)空间中解的存在性,其中max(N,2)ps<+∞.(1)-div(C(x)+|u|2)p-22u+|u|p-2u+g(x,u(x))=fa.e.x∈Ω-〈n,(C(x)+|u|2)p-22u〉∈βx(u(x))a.e.x∈Γ这里f∈Ls(Ω)给定,ΩRN为有界锥形区域,n为Γ的外法向导数,g∶Ω×R→R满足Caratheodory条件且对x∈Γ,βx是正常、凸、下半连续函数φx=φ(x,.)的次微分,其中φ∶Γ×R→R.本文是对笔者以往一些工作的继续和补充.

By using the perturbation results on ranges of nonlinear accretive operators, we study the results on the existence of a solution u∈L^5（Ω）max（N,2）≤P≤5〈＋∞.of nonlinear elliptic boundary value problems （1）{-div{（C（x）＋｜△↓u｜^2p-2/2△↓u）}＋｜u｜p-2^u＋g（x,u（x）=f a,e,x,∈^Ω）-〈n,（C（x）＋｜△↓u｜^2）p-2/2△↓u）xβ∈（u（x））a,e,x∈Г where f∈L^5（Ω） is given, Ω∩→R^N is a bounded conical domain, n denotes the exterior normal derivative to Г,g：Ω×R→Rsatisfies Caratheodory＇s conditions and for each x∈Г,βx is the subdifferential of a suitably defined proper, convex, lower-semi-continouus function ФxФ（x,） where Ф：Г×R→R.This paper is a complement and continuation to some previous works of the author.