zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some results on connecting orbits for a class of Hamiltonian systems. (English) Zbl 0707.58022
The existence of various kinds of connecting orbits is established for the Hamiltonian system $(HS)\quad q''+V'(q)=0$ as well as its time periodic analogue. For the autonomous case, the main assumption is that V has a global maximum, e.g. at $x=0$. Variational methods then establish the existence of various kinds of orbits terminating at $x=0$. For the time dependent case it is assumed that V has a local but not global maximum at $x=0$ and it is proved that (HS) has a homoclinic orbit emanating from and terminating at 0.
Reviewer: P.H.Rabinowitz

37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
58E30Variational principles on infinite-dimensional spaces
Full Text: DOI EuDML
[1] Rabinowitz, P.H.: Periodic and heteroclinic orbits for a periodic Hamiltonian system. Analyse Nonlineaire6, 331--346 (1989) · Zbl 0701.58023
[2] Kozlov, V.V.: Calculus of variations in the large and classical mechanics. Russ. Math. Surv.40, 37--71 (1985) · Zbl 0579.70020 · doi:10.1070/RM1985v040n02ABEH003557
[3] Coti-Zelati, V., Ekeland, I., Sere, E.: A variational approach to homoclinic orbits in Hamiltonian systems. Math. Ann.288, 133--160 (1990) · Zbl 0731.34050 · doi:10.1007/BF01444526
[4] Hofer, H., Wysocki, K.: First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems. (preprint) · Zbl 0702.34039
[5] Rabinowitz, P.H.: Homoclinic orbits for a class of Hamiltonian systems. Proc. Royal Soc. Edinburgh114A, 33--38 (1990) · Zbl 0705.34054
[6] Mawhin, J., Willem, M.: Critical Point Theory and Hamiltonian systems. Berlin Heidelberg New York: Springer 1989 · Zbl 0676.58017
[7] Nehari, Z.: On a class of nonlinear second order differential equations. Trans. Am. Math. Soc.95, 101--123 (1960) · Zbl 0097.29501 · doi:10.1090/S0002-9947-1960-0111898-8
[8] Nehari, Z.: Characteristic values associated with a class of nonlinear second-order differential equations. Acta Math.105, 141--175 (1961) · Zbl 0099.29104 · doi:10.1007/BF02559588
[9] Coffman, C.: A minimum-maximum principle for a class of nonlinear integral equations. J. Anal. Math.22, 391--419 (1969) · Zbl 0179.15601 · doi:10.1007/BF02786802
[10] Hempel, J.A.: Superlinear boundary value problems and nonuniqueness. University of New England, Armidale thesis 1970