On the solutions to weakly coupled system of ki-Hessian equations

Abstract

In this paper, the existence and multiplicity of nontrivial radial convex solutions to general coupled system of ki-Hessian equations in a unit ball are studied via a fixed-point theorem. In particular, we obtain the uniqueness of nontrivial radial convex solution and nonexistence of nontrivial radial k-admissible solution to a power-type system coupled by ki-Hessian equations in a unit ball. Moreover, using a generalized Krein-Rutman theorem, the existence of k-admissible solutions to an eigenvalue problem in a general strictly (k−1)-convex domain is also obtained.