Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential
type: Item
instance of: scholarly article
title: Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential
zbMATH Open document ID: 1236.34022
author: Nikolaos S. Papageorgiou
author: Dumitru Motreanu
author: V. V. Motreanu
published in: Communications on Pure and Applied Analysis
publication date: 2011-12-19T00:00:00Z
review text: The paper studies the boundary value problem for the second order periodic system \[ -u''(t)-A(t)u(t)\in \partial F(t,u(t))\quad \text{ a.e. } t\in [0,b],\quad u(0)=u(b),\quad u'(0)=u'(b), \] where \(F:[0,b]\times {\mathbb R}^n\to {\mathbb R}\) is a measurable function, locally Lipschitz in the second variable, \( \partial F(t,x)\) is the Clarke generalized subdifferential of the locally Lipschitz map \(F(t,.)\) and \(A(.)\) is a continuous map from \([0,b]\) into the space of symmetric \((n\times n)\) - matrices. When \(\partial F(t,.)\) has linear growth both near the origin and near infinity and the linear differential operator \(u\to -u''-A(.)u\) has a nontrivial negative spectrum it is proved that the system considered has at least two nontrivial solutions. The proof essentially uses a nonsmooth variant of the reduction method and the nonsmooth critical point theory.
reviewed by: Aurelian Cernea
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 58E50
zbMATH DE Number: 5989670
zbMATH Keywords: resonant system
zbMATH Keywords: indefinite linear part
zbMATH Keywords: reduction method
zbMATH Keywords: coercive functional
zbMATH Keywords: local linking
zbMATH Keywords: \(C\)-condition
MaRDI profile type: Publication
full work available at URL: cpaa.2011.10.1401
OpenAlex ID: W2325114724
DOI: 10.3934/CPAA.2011.10.1401
description: scientific article; zbMATH DE number 5989670