Periodic solutions of second order Hamiltonian systems bifurcating from infinity
2006; Elsevier BV; Volume: 24; Issue: 3 Linguagem: Inglês
10.1016/j.anihpc.2006.03.003
ISSN1873-1430
AutoresJustyna Fura, Sławomir Rybicki,
Tópico(s)Differential Equations and Numerical Methods
ResumoThe goal of this article is to study closed connected sets of periodic solutions, of autonomous second order Hamiltonian systems, emanating from infinity.The main idea is to apply the degree for SO(2)-equivariant gradient operators defined by the second author in [S.Rybicki, SO(2)-degree for orthogonal maps and its applications to bifurcation theory, Nonlinear Anal.TMA 23 (1) (1994) 83-102].Using the results due to Rabier [P.Rabier, Symmetries, topological degree and a theorem of Z.Q.Wang, Rocky Mountain J. Math.24 (3) (1994) 1087-1115] we show that we cannot apply the Leray-Schauder degree to prove the main results of this article.It is worth pointing out that since we study connected sets of solutions, we also cannot use the Conley index technique and the Morse theory.
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