(Iq)–Stability and Uniform Convergence of the Solutions of Singularly Perturbed Boundary Value Problems

Autor:	Robert Vrabel
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	second-order ordinary differential equation boundary value problem Neumann conditions periodic conditions three- and four-point conditions singular perturbation Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 12, p 2717 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11122717
Popis:	In this paper, using the notion of (Iq)–stability and the method of a priori estimates, known as the method of lower and upper solutions, the sufficient conditions guaranteeing uniform convergence of solutions to the solution of a reduced problem on the entire interval [a,b] have been established for four different types of boundary conditions for a singularly perturbed differential equation εy″=f(x,y,y′), a≤x≤b. In the second part of the paper, by employing the Peano phenomenon, we analyzed the structure of the solutions of the reduced problem f(x,y,y′)=0.
Databáze:	Directory of Open Access Journals
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