Abstract: Using the method of upper and lower solutions, we discuss the existence and uniqueness of positive radial solutions for elliptic boundary value problems with gradient term:When the coefficient function K(r)=O(1/r^2(N-1))(r→+∞), under the condition that the nonlinear term f(r,u,η） satisfies some appropriate inequality conditions and Nagumo condition on η, we prove the existence and uniqueness of the positive radial solution of the problem.

Key words: elliptic boundary value problem, positive radial solution, exterior domain, Nagumo condition, upper solution, lower solution