Nonlinear ordinary boundary value problems under a combined effect of periodic and attractive nonlinearities
type: Item
instance of: scholarly article
title: Nonlinear ordinary boundary value problems under a combined effect of periodic and attractive nonlinearities
zbMATH Open document ID: 0952.34013
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-01-15T00:00:00Z
review text: The author studies the following boundary value problems: \[ -u''(t)- u(t)+ f(u(t))+ g(u(t))= h(t),\quad t\in [0,\pi],\quad u(0)= u(\pi)= 0,\tag{1} \] and \[ -u''(t)- au(t)+ (a- 1)v(t)+ f(v(t))= p(t),\tag{2} \] \[ -v''(t)- av(t)+ (a- 1)u(t)+ g(u(t))= q(t),\quad t\in [0,\pi), \] \[ u(0)= u(\pi)= v(0)= v(\pi)= 0, \] where \(f: \mathbb{R}\to\mathbb{R}\) is a continuous \(T\)-periodic function and \(\int^T_0 f(s) ds= 0\); \(g: \mathbb{R}\to\mathbb{R}\) is a continuous bounded function and \(g(u)u\leq 0\), \(\forall u\in\mathbb{R}\) or \(g(u)u\geq 0\), \(\forall u\in\mathbb{R}\); \(h\in C[0,\pi]\); \(a\) is a real constant; \(p(t)\), \(q(t)\) are functions for which there exist the functions \(u,v\in C^2[0,\pi]\) so that \[ -u''(t)- au(t)+ (a- 1)v(t)= p(t), \] \[ -v''(t)- av(t)+ (a- 1)u(t)= q(t),\quad t\in [0,\pi], \] \[ u(0)= u(\pi)= v(0)= v(\pi)= 0. \] It is proved the existence of solutions to these problems, using the alternative method.
reviewed by: Ion Onciulescu
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1429700
zbMATH Keywords: nonlinear ordinary boundary value problems
zbMATH Keywords: periodic and attractive nonlinearities
author: Antonio Cañada
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6689
OpenAlex ID: W2065450285
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DOI: 10.1006/JMAA.1999.6689
description: scientific article; zbMATH DE number 1429700