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New existence and multiplicity theorems of periodic solutions for non-autonomous second order Hamiltonian systems

Authors
Journal
Mathematical and Computer Modelling
0895-7177
Publisher
Elsevier
Publication Date
Volume
46
Identifiers
DOI: 10.1016/j.mcm.2006.11.019
Keywords
  • Critical Point
  • Periodic Solution
  • Second Order Hamiltonian System
  • Sobolev’S Inequality
Disciplines
  • Mathematics

Abstract

Abstract In the present paper, the non-autonomous second order Hamiltonian systems (1) { u ̈ ( t ) = ∇ F ( t , u ( t ) ) , a.e. t ∈ [ 0 , T ] u ( 0 ) − u ( T ) = u ̇ ( 0 ) − u ̇ ( T ) = 0 , are studied and a new existence theorem and a new multiplicity theorem of periodic solutions are obtained.

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