On Sumudu transform and general integro quasi- differential equations

Abstract

In this paper, we have considered the problem that all solutions of the general integro quasi-differential equation $[\tau -\lambda I]y(t)=wF(t,y,S(y))$ are bounded and $L_{w}^{2}$- bounded on $[0,b)$ under
suitable conditions on the integrand function F, where $\tau $ is a general quasi-differential expression of order $n$ with complex coefficients and $S(y)$ is the Sumudu transform of the function $y$.