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

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).