Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1077.34069
Boichuk, Alexander A.; Grammatikopoulos, Myron K.
Perturbed Fredholm boundary value problems for delay differential systems. (English)
[J] Abstr. Appl. Anal. 2003, No. 15, 843-864 (2003). ISSN 1085-3375; ISSN 1687-0409/e

The considered linear boundary value problem with a small parameter $\varepsilon$ has the form $$\dot z(t)=\sum^k_{i=1} A_i(t)z(h_i(t))+\varepsilon\sum^k_{i=1}B_i(t)z(h_i(t))+g(t),\quad t\in [a,b];\ z(s)=\psi(s), \ s<\alpha; \ \ell z=\alpha.$$ The unknown solution $z$ takes values in a finite-dimensional space. The functions $h_i(t)\le t$ are measurable. In case $h_i(t)<\alpha$, it is assumed that $z(h_i(t))=\psi(h_i(t))$. The boundary conditions are described by the bounded linear operator $\ell$. The Fredholm properties of the boundary value problem are obtained in the form of power series in $\varepsilon$. Examples are given.
[Sergei A. Brykalov (Ekaterinburg)]

MSC 2000:: *34K10 Boundary value problems for functional-differential equations
34K06 Linear functional-differential equations

Keywords: linear boundary value problem; linear functional-differential equation; small parameter

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