Upper and lower solution method and a singular boundary value problem for the one-dimensional \(p\)-Laplacian
type: Item
instance of: scholarly article
title: Upper and lower solution method and a singular boundary value problem for the one-dimensional \(p\)-Laplacian
zbMATH Open document ID: 0977.34016
author: Daqing Jiang
author: Wenjie Gao
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-01-07T00:00:00Z
review text: The authors study the singular boundary value problem for the one-dimensional \(p\)-Laplacian \[ (\Phi (u'))' = - g(t,u) \text{ for all } t \in (0,1), \quad u(0)=u(1)=0, \] with \(\Phi(s) = \mid s \mid^{p-2} s\) and \(p > 1\). The singularity may appear at \(u=0\), \(t =0\) and \(t= 1\) and the function \(g\) may change sign. The authors prove that if there exist a lower solution \(\alpha\) and an upper solution \(\beta\) such that \(\alpha \leq \beta\), then this problem has at least one solution lying between both functions. Such solution is given as the limit of a sequence of solutions to nonsingular truncated problems. Finally, the authors give different existence and uniqueness results derived from the previous existence results.
reviewed by: Alberto Cabada
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1563084
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: \(p\)-Laplacian problem
zbMATH Keywords: singular problem
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7012
OpenAlex ID: W2092187160
cites work: Singular boundary value problems for superlinear second order ordinary and delay differential equations
cites work: Nonlinear superlinear singular and nonsingular second order boundary value problems
cites work: Singular boundary value problems
cites work: Solvability of some nonlinear boundary value problems
cites work: Some singular, nonlinear differential equations arising in boundary layer theory
cites work: Radially symmetric solutions of a class of singular elliptic equations
cites work: Pairs of positive solutions for the one-dimensional p-Laplacian
cites work: Singular nonlinear boundary value problems for second-order ordinary differential equations
cites work: Krasnoselskii's theorem on operators compressing a cone: Application to some singular boundary value problems
cites work: Upper and lower solutions for a generalized Emden-Fowler equation
cites work: A generalized Emden-Fowler equation with a negative exponent
cites work: On the existence of nonnegative radial solutions for p-Laplacian elliptic systems
cites work: Time-mappings and multiplicity of solutions for the one-dimensional p-Laplacian
cites work: Positive solutions to singular and non-singular second-order boundary value problems
cites work: Some General Existence Principles and Results for $(\phi (y')) = qf(t,y,y'),0 < t < 1$
cites work: SINGULAR DIRICHLET BOUNDARY VALUE PROBLEMS—I. SUPERLINEAR AND NONRESONANT CASE
cites work: A nonlinear singular boundary value problem
cites work: Q3822507
cites work: On positive solutions of singular nonlinear two-point boundary value problems
cites work: Boundary value problems for general second order equations and similarity solutions to the Rayleigh problem
cites work: A singular boundary value problem for the one-dimensional \(p\)-Laplacian
cites work: A unified approach to some two-point, three-point, and four-point boundary value problems with Carathéodory functions
cites work: The existence of positive solutions to a singular nonlinear boundary value problem
cites work: Q3154095
DOI: 10.1006/JMAA.2000.7012
Recommended article: Q4791589
Recommended article: Q4814953
Recommended article: Upper and lower solutions method and a singular superlinear boundary value problem for the one-dimensional \(p\)-Laplacian
Recommended article: A Generalized Upper and Lower Solution Method for Singular Discrete Boundary Value Problems for the One-Dimensional p-Laplacian
Recommended article: Q4543662
Recommended article: Upper and lower solutions method for a class of singular fractional boundary value problems with \(p\)-Laplacian operator
Recommended article: Upper and lower solutions method and a superlinear singular boundary value problem
Recommended article: Q4605027
Recommended article: A singular boundary value problem for the one-dimensional \(p\)-Laplacian
Recommended article: Upper and lower solutions for singular problems with nonlinear boundary data
description: scientific article; zbMATH DE number 1563084