Existence and multiplicity of radial solutions for a k-Hessian system

Abstract

In this paper, we consider the following nonlinear k-Hessian system{Sk(σ(D2z1))=λb(|x|)φ(−z1,−z2), inΩ,Sk(σ(D2z2))=μh(|x|)ψ(−z1,−z2), inΩ,z1=z2=0, on∂Ω, where λ,μ>0, Ω stands for the open unit ball in RN and Sk(σ(D2z)) is the k-Hessian operator of z. Under the appropriate assumptions on φ and ψ, the existence and multiplicity of the k-convex radial solutions are obtained. The method of proving theorems is the Guo-Krasnosel'skii fixed point theorem in a cone.