Existence and uniqueness of nontrivial radial solutions for k-Hessian equations

Abstract

We prove existence and uniqueness of nontrivial radial solutions to the k-Hessian problem{Sk(D2u)=λf(−u)inΩ,u=0on∂Ω, where Sk(D2u) is the k-Hessian operator of u, Ω is the open unit ball in Rn, f is a continuous function and may have k-sublinear growth at ∞ with possible k-superlinear growth at 0, and λ is a large parameter.