An extension of Mawhin's continuation theorem and its application to boundary value problems with a \(p\)-Laplacian
type: Item
instance of: scholarly article
title: An extension of Mawhin's continuation theorem and its application to boundary value problems with a \(p\)-Laplacian
zbMATH Open document ID: 1074.34014
author: Weigao Ge
author: Jingli Ren
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
review text: An abstract continuation theorem of coincidence degree type is stated and proved for some relatively compact perturbations of a class of non-invertible nonlinear operators. Applications are given to three-point boundary value problems of the form \[ (|u'|^{p-2}u')' + f(t,u) = 0, \quad u(0)= 0=G(u(\eta),u(1)) \] with \(\eta \in (0,1).\) For example, a solution exists if there exists \(D >0\) such that \[ f(t,D) < 0 < f(t,-D), \quad G(x,D) < 0 < G(x,-D) \] for all \(t \in [0,1]\) and \(|x| \leq D.\)
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 2102597
zbMATH Keywords: continuation theorem
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: three-point boundary value problem
reviewed by: Jean Mawhin
MaRDI profile type: Publication
full work available at URL: j.na.2004.01.007
OpenAlex ID: W1979721821
cites work: Solvability of a multi-point boundary value problem at resonance.
cites work: A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
cites work: Solvability of three point boundary value problems at resonance
cites work: Ordinary differential equations with nonlinear boundary conditions
cites work: A Fredholm-like result for strongly nonlinear second order ODE's
cites work: Multiplicity of solutions for a class of nonlinear second-order equations
cites work: On the existence of harmonic solutions of Liénard systems
cites work: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation
cites work: A second order m-point boundary value problem at resonance
cites work: A sharper condition for the solvability of a three-point second order boundary value problem
cites work: The existence of \(2\pi\)-periodic solutions for Duffing equation \(\ddot x + g(x(t - \tau ))=p(t)\) with delay
cites work: On a nonlocal boundary value problem at resonance
cites work: Q4264050
cites work: The existence of solutions to Sturm-Liouville boundary value problems with Laplacian-like operator.
DOI: 10.1016/J.NA.2004.01.007
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description: scientific article; zbMATH DE number 2102597