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,?,? 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 ?> 0,B is a unit ball,f:[0,?)?R may change its sign and f(0)> 0,the weight function ??C([0,1]?R)changes its sign and ??0.