Saddle point characterization and multiplicity of periodic solutions of non-autonomous second-order systems
type: Item
instance of: scholarly article
title: Saddle point characterization and multiplicity of periodic solutions of non-autonomous second-order systems
zbMATH Open document ID: 1058.34053
author: Xian Wu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-01T00:00:00Z
review text: The paper deals with the following two classes of second-order systems \[ u^{\prime \prime} (t) = \nabla F(t,u(t)) \;\text{a.e.} \;t \in [0,T], \] \[ u(0) - u(T) = u^\prime(0) - u^\prime(T) = 0 \] and \[ u^{\prime \prime} (t) = \beta(t)u(t) + \lambda \nabla F(t,u(t)) \;\text{a.e.} \;t \in [0,T], \] \[ u(0) - u(T) = u^\prime(0) - u^\prime(T) = 0. \] The authors present existence results for these two classes by using the critical point reduction method and the three-critical-point theorem, respectively.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 2105454
zbMATH Keywords: critical point
zbMATH Keywords: nonautonomous second-order systems
zbMATH Keywords: Sobolev's inequality
zbMATH Keywords: periodic solutions
reviewed by: Emil Minchev
MaRDI profile type: Publication
full work available at URL: j.na.2004.05.020
OpenAlex ID: W2010938920
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DOI: 10.1016/J.NA.2004.05.020
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description: scientific article; zbMATH DE number 2105454