The multiplicity of radial k-convex solutions for an augmented Hessian equation

Abstract

In this article, we apply the sub-super-solution method to investigate the multiplicity of radial k-convex solutions to an augmented Hessian problem{Sk(λ(D2u−μI))=b(|x|)g(u),x∈Ω,u=+∞,x∈∂Ω, where Ω⊆RN(N≥2) is a ball, k∈1,2,⋯,N, and μ is a positive constant.