Existence Of Radial Solutions Of Several K-Hessian Equations

In this paper,we study the existence of radial solutions of several kinds of k-Hessian equations,specific as follows:In the first section,based on the fixed-point index theory and the extended Krein-Rutman theorem,we study the existence of radial k-convex solutions for nonlinear k-Hessian equation coupled systemwhere k=1,2,···,N(N≥2),B(?)R~N is a unit ball,α,β are positive constants.In the second section,by using the fixed-point theorem,we consider the existence and multiplicity of radial k-admissible solutions for nonlinear k-Hessian equation coupled systemwhere k=1,2,···,N(N≥2),f_i∈C([0,1]×[0,+∞),[0,+∞))(i=1,2),B={x∈R~N:|x|<1}is a unit ball.In the third section,by applying the Leray-Schauder fixed-point theorem,we consider the existence of positive radial solutions for k-Hessian problem with signchanging weightwhere parameter λ> 0,B is a unit ball,f:[0,∞)→R may change its sign and f(0)> 0,the weight function α∈C([0,1]→R)changes its sign and α≠0.