Existence For Solutions Of A Class Of Hessian Equations

Hessian equation is a class of important nonlinear partial differential equations.Based on previous studies,we investigate the supercritical exponent problem.We prove the existence of radial solutions of ?k(D2u)=(-u)?(k)+f by using Mountain Pass Theorem,where f is the perturbation function.We find the corresponding functional I of the equation.Then we prove that functional I satisfies the required conditions of Mountain Pass Theorem.We prove(PS)condition by(AR)condition.Finally,the radial solution is simply analyzed.