Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1129.39008
Xue, Yan-Fang; Tang, Chun-Lei
Existence of a periodic solution for subquadratic second-order discrete Hamiltonian system. (English)
[J] Nonlinear Anal., Theory Methods Appl. 67, No. 7, A, 2072-2080 (2007). ISSN 0362-546X

Consider the nonlinear second order discrete Hamiltonian system $$ \Delta^2u(t-1)+\nabla F(t,u(t))=0, \quad \forall t\in Z, $$ where $\Delta u(t)=u(t+1)-u(t)$, $\Delta^2u(t)=\Delta (\Delta u(t))$, $F: Z\times R^N\to R$, $F(t,x)$ is continuously differentiable in $x$ for every $t\in Z$ and $T$-periodic in $t$ for all $x\in R^N$, $T$ is a positive integer, $Z$ is the set of all integers, $\nabla F(t,x)$ denotes the gradient of $F(t,x)$ in $x$. Several criteria on the existence of at least one $T$-periodic solution are presented, which are established by employing minimax methods in critical point theory. The obtained results improve some exisiting ones.
[Yuming Chen (Waterloo)]

MSC 2000:: *39A12 Discrete version of topics in analysis
39A11 Stability of difference equations
37J45 Periodic, homoclinic and heteroclinic orbits, etc.

Keywords: periodic solution; critical point; subquadratic system; nonlinear second order discrete Hamiltonian system

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]