Existence and multiplicity results for periodic solutions of superquadratic Hamiltonian systems where the potential changes sign
type: Item
instance of: scholarly article
title: Existence and multiplicity results for periodic solutions of superquadratic Hamiltonian systems where the potential changes sign
zbMATH Open document ID: 0821.34041
DOI: 10.1007/BF01194013
author: Mario Girardi
author: M. Matzeu
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 1995-09-25T00:00:00Z
review text: The paper deals with the existence of periodic solutions of the system (1) \(\ddot x + b(t) V'(x(t)) = 0\) where \(b(t)\) is a continuous \(T\)- periodic \((T > 0)\) real function and \(V\) has a superquadratic behavior. In case that \(b(t)\) changes its sign, some results have been obtained in other papers but under the assumption that \(V\) is homogeneous. Here the case \(\int^ T_ 0 b(t)dt \neq 0\) is considered and the homogeneity assumption on \(V\) is weakened, in the sense that one requires that \(V\) differs from a homogeneous superquadratic function by a quadratic term, outside a sufficiently large sphere. Several theorems which discuss the existence of periodic solutions of equation (1) are proved.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 736849
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: periodic solutions
reviewed by: Bozhidar Cheshankov
MaRDI profile type: Publication
cites work: On semilinear elliptic equations with indefinite nonlinearities
cites work: Solutions of minimal period for a class of convex Hamiltonian systems
cites work: Dual variational methods in critical point theory and applications
cites work: Existence and multiplicity results for homogeneous second order differential equations
cites work: Q4697357
cites work: Q4692985
cites work: Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems
cites work: A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain-Pass Theorem
cites work: Periodic solutions of a second order superquadratic system with a change of sign in the potential
cites work: Extensions of the mountain pass theorem
cites work: Q4155228
cites work: Periodic solutions of second order nonautonomous systems with the potentials changing sign
full work available at URL: https://doi.org/10.1007/bf01194013
OpenAlex ID: W2034207519
description: scientific article; zbMATH DE number 736849