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)
Stability criteria for linear periodic Hamiltonian systems. (English) Zbl 1195.34079
Consider the first order linear system $$x^{\prime }=a(t)x+b(t)u,\quad u^{\prime }=-c(t)x-a(t)u,\quad t\in \Bbb R,\tag$*$ $$ where $a,b$ and $c$ are $T$-periodic real-valued piece-wise continuous functions defined on $\Bbb R$. The system ($*$) is said to be stable if all solutions are bounded on $\Bbb R$, unstable if all nontrivial solutions are unbounded on $\Bbb R$, and conditionally stable if there exists a nontrivial solution bounded on $\Bbb R$. The author obtain new stability criteria for ($*$).

34D20Stability of ODE
37J25Stability problems (finite-dimensional Hamiltonian etc. systems)
Full Text: DOI
[1] Cheng, S. S.: Lyapunov inequalities for differential and difference equations, Fasc. math. 23, 25-41 (1991) · Zbl 0753.34017
[2] Coddington, E. A.; Levinson, N.: Theory of ordinary differential equations, (1955) · Zbl 0064.33002
[3] Guseinov, G. Sh.; Kaymakcalan, B.: Lyapunov inequalities for discrete linear Hamiltonian systems, Comput. math. Appl. 45, 1399-1416 (2003) · Zbl 1055.39029 · doi:10.1016/S0898-1221(03)00095-6
[4] Guseinov, G. Sh.; Zafer, A.: Stability criteria for linear periodic impulsive Hamiltonian systems, J. math. Anal. appl. 335, 1195-1206 (2007) · Zbl 1128.34005 · doi:10.1016/j.jmaa.2007.01.095
[5] Krein, M. G.: Foundations of the theory of $\lambda $-zones of stability of canonical system of linear differential equations with periodic coefficients, Amer. math. Soc. transl. Ser. 2 120, 1-70 (1955) · Zbl 0516.34049
[6] Miller, R. K.; Michel, A. N.: Ordinary differential equations, (1982) · Zbl 0552.34001