×

zbMATH — the first resource for mathematics

Even homoclinic orbits for super quadratic Hamiltonian systems. (English) Zbl 1201.37096
The authors investigate the existence of even homoclinic orbits for the second-order Hamiltonian system \(\ddot{u} +V_u(t,u)=0\), where \(V(t,u)=-K(t,u)+W(t,u)\in C^1({\mathbb R}\times{\mathbb R}^n,{\mathbb R})\), \(K\) is less quadratic and \(W\) is super quadratic in \(u\) at infinity by the solutions of a sequence of nil-boundary-value problems.

MSC:
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Zhang, Symmetrically homoclinic orbits for symmetric Hamiltonian systems, Journal of Mathematical Analysis and Applications 247 (2) pp 645– (2000) · Zbl 0983.37076
[2] Alves, Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation, Applied Mathematics Letters 16 (5) pp 639– (2003) · Zbl 1041.37032
[3] Carriao, Existence of homoclinic solutions for a class of time-dependent Hamiltonian systems, Journal of Mathematical Analysis and Applications 230 (1) pp 157– (1999)
[4] Serra, Subharmonic solutions to second-order differential equations with periodic nonlinearities, Nonlinear Analysis 41 (5-6) pp 649– (2000) · Zbl 0985.34033
[5] Korman, Homoclinic orbits for a class of symmetric Hamiltonian systems, Electronic Journal of Differential Equations 1994 (1) pp 1– (1994) · Zbl 0788.34042
[6] Felmer, Homoclinic and periodic orbits for Hamiltonian systems, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 26 (2) pp 285– (1998) · Zbl 0919.58026
[7] Ou, Existence of homoclinic solution for the second order Hamiltonian systems, Journal of Mathematical Analysis and Applications 291 (1) pp 203– (2004) · Zbl 1057.34038
[8] Salvatore, Homoclinic orbits for a special class of nonautonomous Hamiltonian systems, in: Proceedings of the Second World Congress of Nonlinear Analysts, Part 8 (Athens, 1996), Nonlinear Analysis 30 (8) pp 4849– (1997)
[9] Ding, Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems, Nonlinear Analysis 25 (11) pp 1095– (1995) · Zbl 0840.34044
[10] Ambrosetti, Dual variational methods in critical point theory and applications, Journal of Functional Analysis 14 pp 349– (1973) · Zbl 0273.49063
[11] Ding, Homoclinic orbits for a nonperiodic Hamiltonian system, Journal of Differential Equations 237 (2) pp 473– (2007) · Zbl 1117.37032
[12] Rabinowitz, Some results on connecting orbits for a class of Hamiltonian systems, Mathematische Zeitschrift 206 (3) pp 473– (1991) · Zbl 0707.58022
[13] Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proceedings of the Royal Society of Edinburgh: Section A 114 (1-2) pp 33– (1990) · Zbl 0705.34054 · doi:10.1017/S0308210500024240
[14] Marek, Homoclinic solutions for a class of second order Hamiltonian systems, Journal of Differential Equations 219 (2) pp 375– (2005) · Zbl 1080.37067
[15] Lv, Existence of even homoclinic orbits for second-order Hamiltonian systems, Nonlinear Analysis 67 pp 2189– (2007) · Zbl 1121.37048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.