Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1145.45003
Liu, Zeqing; Kang, Shin Min
Existence and asymptotic stability of solutions to a functional-integral equation. (English)
[J] Taiwanese J. Math. 11, No. 1, 187-196 (2007). ISSN 1027-5487

Using a fixed point theorem of Darbo type in the space of bounded continuous functions, the existence of a bounded solution of the equation $$x(t)=f(t,x(t))+g(t,x(t))\int\sb{0}\sp{t}u(t,s,x(s))\,ds$$ is obtained when $\vert u(t,s,x)\vert\le a(t)b(s)$ with small $a,b$ and $f(t,\cdot)$ and $g(t,\cdot)$ are contractions with small constants $k$ and $m(t)$ where $m(t)a(t)\to0$ sufficiently fast as $t\to\infty$. It is also claimed that the solution $x$ is asymptotically stable; however, the authors mean by this apparently only that the solution is asymptotically unique, i.e.\ any solution $y$ of the {\it same\/} equation (with not too large norm) satisfies $x(t)-y(t)\to0$ as $t\to\infty$.
[Martin Väth (Giessen)]

MSC 2000:: *45G10 Nonsingular nonlinear integral equations
47H09 Mappings defined by "shrinking" properties
45M05 Asymptotic theory of integral equations
45M10 Stability theory of integral equations

Keywords: asymptotic stability; bounded solution; functional-integral equation; condensing operator

Cited in: Zbl 1190.47090

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