Twin nonnegative solutions for higher-order boundary value problems
type: Item
instance of: scholarly article
title: Twin nonnegative solutions for higher-order boundary value problems
zbMATH Open document ID: 0969.34021
DOI: 10.1016/S0362-546X(99)00176-5
author: Ravi P. Agarwal
author: Donal O'Regan
author: V. Lakshmikantham
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-09-25T00:00:00Z
review text: The authors prove the existence of twin nonnegative solutions to the \((p,n-p)\) conjugate problem: \[ (-1)^{n-p} y^{(n)} = \varphi(t) f(t,y), \quad 0< t< 1, \] \[ y^{(i)}(0)= 0, \quad 0\leq i\leq p-1, \qquad y^{(i)}(1)= 0, \quad 0\leq i\leq n-p-1, \] with \(n\geq 2\), \(1\leq p\leq n-1\), and to the \((n,p)\) problem: \[ y^{(n)}+ \varphi(t) f(t,y)= 0, \quad 0< t< 1, \] \[ y^{(i)}(0)= 0, \quad 0\leq i\leq p-2, \qquad y^{(p)}(1)= 0, \quad 1\leq p\leq n-1, \] is fixed with \(n\geq 2\). To do so, they develop a new technique which involves combining existence principles from the literature with Krasnoselskii's fixed-point theorem in a cone. The existence theory given in this paper is very general and extends many results in the literature. Also, the ideas here could be extended to discuss other higher-order problems.
reviewed by: Idris Addou
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1539291
zbMATH Keywords: nonsingular boundary value problems
zbMATH Keywords: nonlinear alternative
zbMATH Keywords: Krasnoselskii's fixed-point theorem
zbMATH Keywords: positive solutions
MaRDI profile type: Publication
cites work: Positive solutions for \((p,n-p)\) conjugate boundary value problems
cites work: Q4230136
cites work: Positive solutions for (n − 1, 1) conjugate boundary value problems
cites work: Multiple positive solutions of some boundary value problems
cites work: On the existence of positive solutions of nonlinear second order differential equations
cites work: Q4337944
cites work: On eigenvalue intervals and twin eigenfunctions of higher-order boundary value problems
cites work: Q4454238
cites work: Eigenvalue characterization for (n · p) boundary-value problems
full work available at URL: s0362-546x(99)00176-5
OpenAlex ID: W1999296264
description: scientific article; zbMATH DE number 1539291