【摘要】 通过构造Green函数,借助锥不动点定理讨论二阶常微分方程两点边值问题u″+u+f(t,u)=0,αu(0)-βu′(0)=0,γu(1)+δu′(1)=0正解的存在性。更多还原

【Abstract】 This paper study the existence of positive solutions of the differential equation u″+F（t,u）=0 with linear boundary conditions. The existence of at least one positive solution was shown if F is neither superlinear nor sublinear by a simple application of a Fixed Point Theorem in cones. In this paper, the second-order boundary value problem（BVP） was considered. u″+F（t,u）=0, 0<t<1,（1.1） αu（0）-βu′（0）=0, γu（1）+δu′（1）=0（1.2） The following conditions will be assumed throught: （a） F∈C（[0,1]×[0,∞）), （b） α,β,γ,δ≥0 （c） 0≤arcsin（βα²+β²）≤π2-1, 0≤arcsin（δγ²+δ²）≤π2-1. The BVP （1.1）,（1.2） arises in many different areas of applied mathematics and physics. Additional existence results may be found in lienture^[2-6].Our purpose here is to give an existence result for positive solutions to the BVP（1.1）,（1.2）assuming that F is neither superlinear nor sublinear.更多还原