Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions
type: Item
instance of: scholarly article
title: Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions
zbMATH Open document ID: 0964.34016
DOI: 10.1016/S0362-546X(99)00158-3
author: Alberto Cabada
author: Rodrigo L. Pouso
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-06-28T00:00:00Z
review text: The authors study a \(\phi\)-Laplacian problem with nonlinear functional boundary conditions and discontinuous right-hand side \(f\). Assuming that \(f\) satisfies an appropriate Nagumo condition, they prove the existence of at least one solution to this problem using the method of upper and lower solutions. Moreover, they prove the existence of extremal solutions and apply the monotone iterative technique by assuming certain additional hypotheses. The results obtained widely improve those from a previous paper by the same authors [Nonlinear Anal., Theory Methods Appl. 35A, No. 2, 221-231 (1999; Zbl 0920.34029)].
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1532914
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: \(\phi\)-Laplacian
zbMATH Keywords: discontinuous ordinary differential equations
zbMATH Keywords: monotone method
zbMATH Keywords: Nagumo condition
MaRDI profile type: Publication
cites work: Q5758481
cites work: Q4040886
cites work: An introduction to nonlinear boundary value problems
cites work: Q4748596
cites work: The monotone method for second order problems with linear and nonlinear boundary conditions
cites work: Existence result for the problem (φ(u′))′ = f(t, u, u′) with periodic and Neumann boundary conditions
cites work: Existence results for the problem (φ(u′))′=f(t,u,u′) with nonlinear boundary conditions
cites work: Monotone iterative methods for boundary value problems
cites work: Pairs of positive solutions for the one-dimensional p-Laplacian
cites work: Upper and lower solutions for second-order boundary value problems with nonlinear boundary conditions
cites work: On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions
cites work: A Fredholm-like result for strongly nonlinear second order ODE's
cites work: Boundary value problems of a class of quasilinear ordinary differential equations
cites work: Q5691206
cites work: Q4303531
cites work: Q4064235
cites work: Q3807603
cites work: Q4143788
cites work: Integration in linear spaces
cites work: Some General Existence Principles and Results for $(\phi (y')) = qf(t,y,y'),0 < t < 1$
cites work: Q3901719
cites work: Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions
cites work: Existence of solutions to boundary value problems for a nonlinear second order equation with weak Carathéodory functions
Wikidata QID: Q126351679
description: scientific article; zbMATH DE number 1532914