Singular boundary value problems for the image-Laplacian Original Research Article

We prove the existence of a large positive solution for the boundary value problems View the MathML source{−Δpu=λ(−h(u)+g(x,u))in Ω,u=0on ∂Ω, Turn MathJax on where View the MathML sourceΔpu=div(|∇u|p−2∇u),p>1,Ω is a bounded domain in RN,λRN,λ is a positive parameter, g(x,.)g(x,.) is (p−1)(p−1)-subhomogeneous at ∞∞, and hh is allowed to become ∞∞ at u=0u=0. Results for related systems are also discussed.