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).