Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2018 / Cilt: 2 - Sayı: 3

Uniqueness of solutions of boundary value problems at resonance

Pages
168–183
Publication Date
2018-09-30
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Two examples are provided in which explicit upper and lower solutions are exhibited.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, the method of upper and lower solutions is employed to obtain uniqueness of solutions for a boundary value problem at resonance.
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Key Findings & Data:The shift method is applied to show the existence of solutions.
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Conclusion & Impact:Two examples are provided in which explicit upper and lower solutions are exhibited.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:boundary value problem at resonance · shift method · upper and lower solutions

Abstract

In this paper, the method of upper and lower solutions is employed to obtain uniqueness of solutions for a boundary value problem at resonance. The shift method is applied to show the existence of solutions. A monotone iteration scheme is developed and sequences of approximate solutions are constructed that converge monotonically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

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Cite This Article

ALJEDANİ, J., ELOE, P. (2018). Uniqueness of solutions of boundary value problems at resonance. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 2 - Sayı: 3, 168–183. https://ajindex.com/articles/729169

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