Upper and lower solutions method for a class of second-order coupled systems

This paper provides a class of upper and lower solution definitions for second-order coupled systems by transforming the fourth-order differential equation into a second-order differential system. Then, by constructing a homotopy parameter and utilizing the maximum principle, we propose an upper and...

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Veröffentlicht in:	Boundary value problems 2024-02, Vol.2024 (1), p.30-8, Article 30
Hauptverfasser:	Yu, Zelong, Bai, Zhanbing, Shang, Suiming
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Approximations and Expansions Boundary conditions Boundary value problems Coupled system Degree theory Difference and Functional Equations Differential equations Dirichlet problem Lower and upper solutions Mathematics Mathematics and Statistics Maximum principle Ordinary Differential Equations Partial Differential Equations
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Zusammenfassung:	This paper provides a class of upper and lower solution definitions for second-order coupled systems by transforming the fourth-order differential equation into a second-order differential system. Then, by constructing a homotopy parameter and utilizing the maximum principle, we propose an upper and lower solutions method for studying a class of second-order coupled systems with Dirichlet boundary conditions and obtain an existence result.
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-024-01837-3