International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 421561 | https://doi.org/10.1155/S0161171203008007

Sobhy El-Sayed Ibrahim, "On the Lw2-boundedness of solutions for products of quasi-integro differential equations", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 421561, 21 pages, 2003. https://doi.org/10.1155/S0161171203008007

On the Lw2-boundedness of solutions for products of quasi-integro differential equations

Received14 Aug 2001

Abstract

Given a general quasi-differential expressions τ1,τ2,,τn each of order n with complex coefficients and their formal adjoints are τ1+,τ2+,,τn+ on [0,b), respectively, we show under suitable conditions on the function F that all solutions of the product of quasi-integrodifferential equation [j=1nτj]y=wF(t,y,0tg(t,s,y,y,,y(n21)(s))ds) on [0,b), 0<b;t,s0, are bounded and Lw2-bounded on [0,b). These results are extensions of those by Ibrahim (1994), Wong (1975), Yang (1984), and Zettl (1970, 1975).

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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