Existence of positive solutions of third-order boundary value problems with integral boundary conditions in Banach spaces

Dan Fu; Wei Ding

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Existence of positive solutions of third-order boundary value problems with integral boundary conditions in Banach spaces

机译：Banach空间中带积分边界条件的三阶边值问题正解的存在性

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This paper deals with positive solutions of a third-order differential equation in ordered Banach spaces, ( φ ( ? x ″ ( t ) ) ) ′ = f ( t , x ( t ) ) , t ∈ J , subject to the following integral boundary conditions: x ( 0 ) = θ , x ″ ( 0 ) = θ , x ( 1 ) = ∫ 0 1 g ( t ) x ( t ) d t , where θ is the zero element of E, g ∈ L [ 0 , 1 ] is nonnegative, φ : R → R is an increasing and positive homomorphism, and φ ( 0 ) = θ 1 . The arguments are based upon the fixed-point principle in cone for strict set contraction operators. Meanwhile, as an application, we also give an example to illustrate our results.

机译：本文讨论了有序Banach空间中的三阶微分方程的正解（φ（？x”（t）））'= f（t，x（t）），t∈J，服从以下积分边界条件：x（0）=θ，x''（0）=θ，x（1）=∫0 1 g（t）x（t）dt，其中θ是E的零元素，g∈L [0 ，1]为非负，φ：R→R为递增正正同态，φ（0）=θ1。对于严格的集合收缩算子，参数基于圆锥体中的定点原理。同时，作为一个应用程序，我们还给出一个例子来说明我们的结果。

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《Advances in Difference Equations》 |2013年第1期|共12页
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Dan Fu; Wei Ding;
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机译：Banach空间中带积分边界条件的三阶边值问题正解的存在性

Existence of positive solutions of third-order boundary value problems with integral boundary conditions in Banach spaces

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