Abstract
AbstractThis paper is concerned with the existence of periodic solutions for asymptotically linear second-order delay differential equations. We will establish an index theory for the linear system directly in the sense that we do not need to change the problem of the original linear system into the problem of an associated Hamiltonian system. By using the critical point theory and the index theory, some new existence results are obtained.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference44 articles.
1. Abbondandolo, A.: Morse Theory for Hamiltonian Systems. Chapman Hall, London (2001)
2. Amann, H., Zehnder, E.: Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Ann. Sc. Norm. Super. Pisa, Cl. Sci. 7, 539–603 (1980)
3. Bartsch, T., Ding, Y.: Deformation theorems on non-metrizable vector spaces and applications to critical point theory. Math. Nachr. 279, 1267–1288 (2006)
4. Benci, V., Rabinowitz, P.H.: Critical point theorems for indefinite functionals. Invent. Math. 53, 241–273 (1979)
5. Progr. Nonlinear Differential Equations Appl.;K.C. Chang,1993