On a periodic-type boundary value problem for first-order nonlinear functional differential equations
type: Item
instance of: scholarly article
title: On a periodic-type boundary value problem for first-order nonlinear functional differential equations
zbMATH Open document ID: 1022.34058
DOI: 10.1016/S0362-546X(01)00838-0
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-09-30T00:00:00Z
review text: Here, the solvability and the unique solvability of the boundary value problem \[ u'(t)= F(u)(t),\quad u(a)-\lambda u(b)= h(u),\tag{\(*\)} \] are discussed, where \(F\in K_{ab}\), \(K_{ab}\) is the set of continuous operators \(F: C([a, b],\mathbb{R})\to L([a,b]),\mathbb{R})\) satisfying the Carathéodory condition, that is, for every \(r> 0\) there exists \(q_r\in L([a, b],\mathbb{R}_+)\) such that \[ |F(v)(t)|\leq q_r(t)\text{ for }t\in [a,b],\quad\|v\|_C\leq r, \] \(\lambda\in \mathbb{R}_+\) and \(h: C([a, b],\mathbb{R})\to \mathbb{R}\) is continuous. Different types of sufficient conditions are obtained for the solvability of \((*)\). Examples are given to illustrate the results obtained.
Mathematics Subject Classification ID: 34K10
zbMATH DE Number: 1810000
zbMATH Keywords: periodic-type boundary value problem
zbMATH Keywords: first-order nonlinear functional-differential equations
zbMATH Keywords: solvability
author: Robert Hakl
author: Alexander Lomtatidze
author: Jiří Šremr
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00838-0
OpenAlex ID: W2077657755
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description: scientific article; zbMATH DE number 1810000