Integral equations, Volterra equations, and the remarkable resolvent: contractions

T. A. Burton, Northwest Research Institute, Port Angeles, WA, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 2. (2006), pp. 1-17.

Abstract: This paper concerns several variants of an integral equation
$$ x(t)=a(t)-\int^t_0 C(t,s) x(s)ds $$, a resolvent $$ R(t,s) $$, and a variation-of-parameters formula
$$ x(t)=a(t)-\int^t_0 R(t,s) a(s)ds $$ with special accent on the case in which $a(t)$ is unbounded. We use contraction mappings to establish close relations between $a(t)$ and $\int^t_0R(t,s) a(s)ds$.

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