Radial Solutions For Elliptic Boundary Value Problems With Gradient Terms In Exterior Domains Of Ball

In this paper,we discuss the existence and uniqueness of radial solutions for the elliptic boundary value problems with gradient termswhere Ω={x∈RN:|x|>R0},N≥ 3,R0>0,K:[R0,∞)→R+ and f:[R0,∞)×R×R+→R are continuous.When the coefficient function K(r)=O(1/r2(N-1))(r→+∞),the existence and uniqueness of radial solutions of the problem are obtained by using Leray-Schauder fixed point theorem,the method of upper and lower solution,truncation function technique and Schauder fixed point theorem.The main results of this paper are as follows:1.Under the condition that the nonlinear term f satisfies linear growth,the existence and uniqueness of radial solutions are obtained by using Leray-Schauder fixed point theorem;2.Under the condition that the nonlinear term f(r,u,η)satisfies one side superlinear growth and Nagumo-type growth on η,using Leray-Schauder fixed point theorem,the existence and uniqueness of radial solutions are obtained;3.Introducing the Nagumo condition,the existence of the radial solution are obtained by using the method of upper and lower solution and truncation function technique.Under the condition that the nonlinear term f(r,u,η)satisfies some appropriate inequalities and Nagumo-type growth on η,the existence and uniqueness of the positive radial solution are obtained by using the method of upper and lower solution;4.By selecting a suitable convex closed set and under relatively weak condi-tions,using Schauder fixed point theorem,the existence and uniqueness of radial solutions are obtained.