Existence and uniqueness results for some nonlinear boundary value problems
type: Item
instance of: scholarly article
title: Existence and uniqueness results for some nonlinear boundary value problems
zbMATH Open document ID: 0855.34021
author: Hai Dang
author: S. F. Oppenheimer
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-02-16T00:00:00Z
review text: The authors are interested in the existence and uniqueness of solutions to the equation (1) \((\varphi (u'))' + k(t) \varphi (u') + f(t,u,u') = 0\), \(a < t < b\), subject to one of the following sets of boundary conditions: (2) \(u(a) = u(b) = 0\) (Dirichlet), (3) \(u'(a) = u'(b) = 0\) (Neumann), (4) \(u(a) = u(b)\) and \(u'(a) = u'(b)\) (periodic). Here \(\varphi : \mathbb{R} \to \mathbb{R}\) is an odd increasing homeomorphism, \(k : [a,b] \to \mathbb{R}\), and \(f : [a,b] \times \mathbb{R}^2 \to \mathbb{R}\). The authors establish existence results for (1) with each of the above boundary conditions, (2), (3), and (4) under various growth conditions on \(f\).
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 902485
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: boundary conditions
reviewed by: Prem N. Bajaj
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0066
OpenAlex ID: W2091720966
DOI: 10.1006/JMAA.1996.0066
description: scientific article; zbMATH DE number 902485