The freezing method for Volterra integral equations in a Banach space

M. I. Gil', Ben Gurion University of the Negev, Beer-Sheva, Israel

E. J. Qualitative Theory of Diff. Equ., No. 17. (2008), pp. 1-7.

Abstract: The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type $$ x(t)- \int_0^t K(t, t-s)x(s)ds =f(t)\;(t\geq 0),$$ where $K(t,s)$ is an operator valued function "slowly" varying in the first argument. Besides, sharp explicit stability conditions are derived.

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