Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

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

Highlights
Master Server