二阶非线性积分边值问题正解的存在唯一性

Existence and uniqueness of positive solutions for second-order nonlinear integral boundary value problem

本文运用双度量空间中的广义Krasnoselskii’s压缩不动点定理研究了二阶非线性积分边值问题u″+a(t)f(t,u(t),u′(t))=0,t∈(0,1),u(0)=0,u(1)=α∫^η0u(s)ds正解的存在唯一性,其中0<η<1,0<α<2/η^2,a∈C([0,1]×[0,∞)×R→[0,∞)连续,且当t0∈[η,1]时a(t0)>0.

In this paper, by using the method of generalized Krasnoselskii’s contractive fixed point theorem in bimetric spaces, we study the existence and uniqueness of the positive solutions for the followingsecond-order nonlinear integral boundary value problem u″+a(t)f(t,u(t),u′(t))=0, t∈(0,1), u(0)=0, u(1)=α∫^η0u(s)ds where 0<η<1,0<α<2/η^2,a∈C([0,1]×[0,+∞)×R→[0,+∞) is continuous and a(t0)>0 when t0∈[η,1].