On a class of second order differential inclusions driven by the scalar \(p\)-Laplacian
type: Item
instance of: scholarly article
title: On a class of second order differential inclusions driven by the scalar \(p\)-Laplacian
zbMATH Open document ID: 1192.34020
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-01-12T00:00:00Z
review text: The authors study a class of nonlinear boundary value problems for second order differential inclusions. In particular they consider the problem: \[ (|x'(t)|^{p-2}x'(t))'\in Ax(t)+F(t,x(t),x'(t))+\theta(x(t)) \text{ a.e. on } T=[0,b], \] \[ x'(0)\in \xi_1(x(0)), -x'(b)\in \xi_2(x(b)), 2 \leq p <+\infty, \] where \(A:D(A)\subset \mathbb R \to 2^{\mathbb R}\backslash {\emptyset}\), \(\xi_{i}:D(\xi_{i})\subset \mathbb R \to 2^{\mathbb R}\backslash {\emptyset}\), \(i=1,2\), are maximal monotone operators, \(\theta:\mathbb R \to \mathbb R\) is a function and \(F:T\times \mathbb R^2 \to 2^{\mathbb R}\backslash {\emptyset}\) is a multivalued map upper semicontinuous in the second variable. By using fixed point techniques combined with the method of lower and upper solutions, the authors prove some existence results of extremal (greatest and smallest) solutions in the ordered interval delimited by the lower and the upper solution.
reviewed by: Francesca Papalini
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 47D60
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5656697
zbMATH Keywords: Sobolev space
zbMATH Keywords: ordered Banach space
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: upper semicontinuous map
zbMATH Keywords: completely continuous operator
zbMATH Keywords: fixed point
zbMATH Keywords: maximal monotone map
zbMATH Keywords: Yosida approximation.
author: Qing-Hua Zhang
author: Gang Li
MaRDI profile type: Publication
full work available at URL: j.na.2009.06.041
OpenAlex ID: W2028287929
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DOI: 10.1016/J.NA.2009.06.041
description: scientific article; zbMATH DE number 5656697