Existence theorems for nonlinear second-order three-point boundary value problems involving the distributional Henstock-Kurzweil integral

You, Xiao‐Zeng; Liu, Wei; Ye, Guoju; Zhao, Dafang

doi:10.22436/jnsa.010.04.42

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2019

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“…The existence questions for such problems have been studied by various authors. For example, this problem for the second-order multipoint boundary value problems have been studied in [5,8,17,18] and references therein. We can note also Gupta [6] where the existence of solutions for the generalized multi-point boundary-value problem is studied.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solutions for the first-order non-linear differential equations with three-point boundary conditions

Mardanov

Sharifov

Ismayilova

2019

Filomat

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In this paper the existence and uniqueness of the solutions to boundary value problems for the first order non-linear system of the ordinary differential equations with three-point boundary conditions are investigated. For the first time the Green function is constructed and the considered problem is reduced to the equivalent integral equations that allow us to prove the existence and uniqueness theorems in differ from existing works, applying the Banach contraction mapping principle and Schaefer's fixed point theorem. An example is given to illustrate the obtained results.

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