On periodic boundary value problem for the equation \(u^{\prime\prime} = f(t,u,u^{\prime})\) with one-sided growth restrictions on \(f\)
type: Item
instance of: scholarly article
title: On periodic boundary value problem for the equation \(u^{\prime\prime} = f(t,u,u^{\prime})\) with one-sided growth restrictions on \(f\)
zbMATH Open document ID: 1004.34012
DOI: 10.1016/S0362-546X(00)00235-2
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-05-15T00:00:00Z
review text: The boundary value problem \[ u''(t)= f(t,u(t), u'(t)),\quad u(a)= u(b),\;u'(a)= u'(b),\tag{P} \] is considered, where \(f: [a,b]\times \mathbb{R}^2\to \mathbb{R}\) satisfies the local Carathéodory conditions. The authors give new sufficient conditions for the solvability of (P) formulated by upper and lower functions and one-sided growth restrictions on the function \(f\) with respect to the third argument. These conditions guarantee the existence of upper and lower solutions to (P) as well. The proofs of existence results are based on new a priori estimates on solutions to second-order differential inequalities with periodic boundary conditions.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1741846
zbMATH Keywords: nonlinear differential equation
zbMATH Keywords: periodic boundary value problem
zbMATH Keywords: upper and lower functions
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: existence
zbMATH Keywords: second-order differential inequalities
author: Ivan Kiguradze
author: Svatoslav Staněk
reviewed by: Ruyun Ma
MaRDI profile type: Publication
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full work available at URL: s0362-546x(00)00235-2
OpenAlex ID: W2020844425
description: scientific article; zbMATH DE number 1741846