单位球上含梯度项的椭圆边值问题径向解的存在性与唯一性

用Schauder不动点定理, 讨论单位球Ω={x∈R^N: |x|<1}上含梯度项的椭圆边值问题径向解的存在性与唯一性,  其中N≥2, f:0,1]×R×R⁺→R连续. 在允许非线性项f(r,ξ,η)关于ξ,η超线性增长的情形下, 获得了该问题径向解及正径向解的存在性结果. 此外，还讨论该问题径向解的唯一性.

Existence and Uniqueness of Radial Solutions to Elliptic Boundary Value Problem with Gradient Terms on the Unit Ball

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.