zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Periodic solutions for a class of non-autonomous Hamiltonian systems. (English) Zbl 1071.34039

Summary: We consider the existence of nontrivial periodic solutions for the superlinear Hamiltonian system

𝒥u ˙-A(t)u+H(t,u)=0,u 2N ,t·

We prove an abstract result on the existence of a critical point for a real-valued functional on a Hilbert space via a new deformation theorem. Different from the work in the literature, the new deformation theorem is constructed under a Cerami-type condition instead of Palais-Smale-type condition. In addition, the main assumption here is weaker than the usual Ambrosetti-Rabinowitz-type condition

0<μH(t,u)u·H(t,u),μ>2,|u|R>0·

This result extends theorems given by S. J. Li and M. Willem [J. Math. Anal. Appl. 189, 6–32 (1995; Zbl 0820.58012)] and S. J. Li and A. Szulkin [J. Differ. Equations 112, 226–238 (1994; Zbl 0807.58040)].


MSC:
34C25Periodic solutions of ODE
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
47J30Variational methods (nonlinear operator equations)
58E05Abstract critical point theory