The existence of radial solutions for a class of k-Hessian systems with the nonlinear gradient terms.

This paper mainly deals with the following k-Hessian system with the nonlinear gradients S k (λ (D 2 u i)) + | ∇ u i | k = φ i (| v | , - u 1 , - u 2 , ... , - u n) , i n Ω , u i = 0 , i = 1 , 2 , ... , n , o n ∂ Ω , where 1 ≤ k ≤ N , n ≥ 2 , Ω is the open unit ball in R N (N ≥ 2) and S k (λ (D 2 u)) is the k-Hessian operator of u. Some results about the existence of radial solutions are obtained by making some appropriate assumptions about R + n -monotone matrices for φ i . Based on the Jensen integral inequality and fixed point theorem, we have overcome the computational difficulties of k-Hessian system with gradients, and obtained the conclusion that the system has at least one radial solution and at least two radial solutions. [ABSTRACT FROM AUTHOR]