International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 10, Pages 639-659
doi:10.1155/S0161171203008007
On the Lw2-boundedness of solutions for products of quasi-integro differential equations
Department of Mathematics, Faculty of Science, Benha University, Kalubia, Benha 13518, Egypt
Received 14 August 2001
Copyright © 2003 Sobhy El-Sayed Ibrahim. 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.
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(n2−1)(s))ds) on [0,b), 0<b≤∞;t,s≥0, 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).