Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4622058 | Journal of Mathematical Analysis and Applications | 2008 | 7 Pages |
Abstract
This paper is concerned with the existence of positive solutions of the singular nonlinear elliptic equation with a Dirichlet boundary condition{Δu=F(x,u)in Ω,u=ϕon ∂Ω, where F is a Borel measurable function in Ω×(0,+∞)Ω×(0,+∞) such that |F(x,u)|⩽V(x)u−α|F(x,u)|⩽V(x)u−α for some α>0α>0 and V satisfying some appropriate conditions. In particular, we show that the above problem has positive solutions whenever inf∂Ωϕinf∂Ωϕ is greater than a positive quantity given by α and V.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Kentaro Hirata,