Abstract: By using Schauder fixed-point theorem, we discuss the existence and uniqueness of radial solutions to elliptic boundary value problem with gradient terms, where Ω={x∈R^N: |x|<1}， N≥2, f: [0,1]×R×R⁺→R is continuous. The existence results of radial solutions and positive radial solutions to the problem are obtained under the condition that the nonlinear term f(r,ξ,η) is allowed to grow superlinearly with respect to ξ and η. In addition, we also discuss the uniqueness of radial solutions of this problem.

Key words: elliptic boundary value problem, unit ball, radial solution, Schauder fixed-point theorem