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Journals / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 4

GREEN'S FUNCTIONAL CONCEPT FOR A NONLOCAL PROBLEM

Kamil ORUÇOĞLU
Kemal ÖZEN
Pages
437–446
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Two illustrative applications are provided

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, by Green's functional concept, in order to obtain Green'ssolution we concentrate on a new constructive technique by which alinear completely nonhomogeneous nonlocal problem for a second-orderloaded differential equation with generally variable coefficients satisfying some general properties such as p-integrability and boundedness istransformed into one and only one integral equation.
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Key Findings & Data:A system of threeintegro-algebraic equations called the special adjoint system is obtainedfor this problem.
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Conclusion & Impact:Two illustrative applications are provided
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this work, by Green's functional concept, in order to obtain Green'ssolution we concentrate on a new constructive technique by which alinear completely nonhomogeneous nonlocal problem for a second-orderloaded differential equation with generally variable coefficients satisfying some general properties such as p-integrability and boundedness istransformed into one and only one integral equation. A system of threeintegro-algebraic equations called the special adjoint system is obtainedfor this problem. A solution of this special adjoint system is Green'sfunctional which enables us to determine Green's function and Green'ssolution for the problem. Two illustrative applications are provided

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Cite This Article

ORUÇOĞLU, K., ÖZEN, K. (2022). GREEN'S FUNCTIONAL CONCEPT FOR A NONLOCAL PROBLEM. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 4, 437–446. https://ajindex.com/articles/530430

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