On the L w 2 -boundedness of solutions for products of quasi-integro differential equations

Sobhy El-Sayed Ibrahim

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-21

Abstract:

Given a general quasi-differential expressions τ 1 , τ 2 , … , τ n each of order n with complex coefficients and their formal adjoints are τ 1 + , τ 2 + , … , τ n + on [ 0 , b ) , respectively, we show under suitable conditions on the function F that all solutions of the product of quasi-integrodifferential equation [ ∏ j = 1 n τ j ] y = w F ( t , y , ∫ 0 t g ( t , s , y , y ′ , … , y ( n 2 − 1 ) ( s ) ) d s ) on [ 0 , b ) , 0 < b ≤ ∞ ; t , s ≥ 0 , are bounded and L w 2 -bounded on [ 0 , b ) . These results are extensions of those by Ibrahim (1994), Wong (1975), Yang (1984), and Zettl (1970, 1975).

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:421561

DOI: 10.1155/S0161171203008007

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