On a two-point boundary value problem for the second order ordinary differential equations with singularities
type: Item
instance of: scholarly article
title: On a two-point boundary value problem for the second order ordinary differential equations with singularities
zbMATH Open document ID: 1027.34022
DOI: 10.1016/S0362-546X(01)00148-1
author: Luisa Malaguti
author: Alexander Lomtatidze
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The authors consider the boundary value problem \[ u''= f(t, u,u'),\tag{1} \] \[ u(a+)= 0,\qquad u(b-)= 0,\tag{2} \] with \(f=\in K_{\text{loc}}(]a,b[\times\mathbb{R}^2;\mathbb{R})\). By a solution to problem (1), (2), the authors understand a function \(u\in\widetilde C_{\text{loc}}'(]a,b[; \mathbb{R})\) satisfying (1) almost everywhere in \(]a,b[\) and also conditions (2). By using a lower solution \(\alpha(t)\) to (1) and an upper solution \(\beta(t)\) to (1), the existence of at least one solution \(u(t)\) to problem (1), (2), is proved, where \(\alpha(t)\leq u(t)\leq \beta(t)\) for \(a\leq t\leq b\).
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 1880111
zbMATH Keywords: second-order singular differential equation
zbMATH Keywords: two-point boundary value problem
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: one-sided restriction
MaRDI profile type: Publication
cites work: Q3836430
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full work available at URL: s0362-546x(01)00148-1
OpenAlex ID: W2027127217
description: scientific article; zbMATH DE number 1880111