Modern Mathematics and Mechanics by Victor A. Sadovnichiy & Michael Z. Zgurovsky

Author:Victor A. Sadovnichiy & Michael Z. Zgurovsky
Language: eng
Format: epub
ISBN: 9783319967554
Publisher: Springer International Publishing

which is also a particular case of the more general Volterra integral equation

(14.3)

The following two theorems, whose proofs were given in 1953 by Sato in [18], are an example of classical results about the existence and uniqueness of solutions for Eq. (14.3), where the relationship between existence and uniqueness of solutions and their attractive character become clear.

Theorem 14.1

Let f be a continuous function on 0 ≤ x ≤ δ, and let

Let h ∈ C(D) have the bound |h(x, s, u)|≤ M in D. Then, if , the integral equation (14.3) has a solution in C([0, r]).

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.