Continuous Dependence of Solutions of Volterra Integral Equations.
BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
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The nonlinear Volterra integral equation is considered. The author discusses topologies on the collection of functions g such that the solution of the equation varies continuously with the data g and f, where the topology on f is the uniform convergence on compact intervals. A necessary and sufficient condition on such a topology for the continuous dependence to hold is given. In a particular case where a Lipschitz condition is added, it is shown that there exists a smallest topology which satisfies the condition. Modified author abstract
- Theoretical Mathematics