一类奇异非线性Dirichlet问题

构造新的精细上下解,结合摄动方法和估计理论,严格刻画了参数β对奇异dirichlet问题-△u=g(x)u-γ+λup,υ＞0,x∈Ω,u| Ω=0古典解的存在性、正则性和渐近行为的影响.其中Ω是RN(N≥1)中的有界区域,γ＞o,λ≥0,p＞0,g∈C loc(Ω),且在Ω上满足boψβ1≤g≤b1ψβ1,β∈R,bo,b1是正常数,φ1是通常的第一特征函数.

A Singular Nonlinear Dirichlet Problem

By constructing the new subsolution and supersolution, and the perturbed method,combining the gstimate argument, we exactly show the parameter β how to affect existence,nonexistence, regularity, and the asymptotic behavior on Ω of the classical solutions to the singular boundary value problem-△u = g(x)u-γ+ λup,u ＞ 0,x ∈Ω,u | Ω = 0, where Ω is a bounded domain with smooth boundary in RN, γ＞ 0,λ≥ 0, p ＞ 0, g ∈ C loc ( Ω ) and bo ψβ1≤ g ≤ b1 ψβ1 on Ω, β∈ R, bo, b1 are positive constants, φ1 is the normal first eigenfunction.