Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1183.34083
Hernández M., Eduardo; Aki, Sueli M.Tanaka
Global solutions for abstract impulsive differential equations. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3-4, A, 1280-1290 (2010). ISSN 0362-546X

The authors consider an impulse differential equation of the sort $$u'(t)= Au(t)+ f(t,u(t)),\quad t\in\bbfR,\quad t\ne t_i,\quad i\in F,$$ $$\Delta u(t_i)= I_i(u(t_i)),\quad i\in F,$$ where $A$ is the infinitesimal generator of a hyperbolic $C_0$-semigroup of bounded linear operators $(T^{(t)})_{t\ge 0}$ on a Banach space $$(X,\Vert.\Vert),\ f: \bbfR\times X\to X,\ I_i: X\to X,\quad i\in F$$ are continuous functions, $F\subset\bbfZ$, $\{t_i: i\in F\}$ is a discrete set of fixed real numbers $t_i< t_j$ for $i< j$. For $t\in [a,b]$, $t\ne tn_i$, $i= 1,\dots, m$ a definition for a mild solution is given. Necessary and sufficient conditions for the boundedness of their solution are given.
[Stepan Kostadinov (Plovdiv)]

MSC 2000:: *34G99 ODE in abstract spaces
34A37 Differential equations with impulses
34D09 Dichotomy, trichotomy
47D06 One-parameter semigroups and linear evolution equations

Keywords: exponential dichotomy; $C_{0}$-semigroup; impulsive 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]