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The generalized quasilinearization for integro-differential equations of Volterra type on time scales. (English) Zbl 1151.39014

The author investigates the following first order integro-differential equation of Volterra type
\[ x^\Delta(t) = f\Big(t,x(t),\int_0^t k(t,s)x(s)\Delta\,s \Big), \quad x(0) = x_0 \]
on a time scale. The symbol \(\Delta\) refers to generalized differentiation resp. integration on time scales (arbitrary nonempty closed subsets of the reals). By the quasilinearization method, based on the idea of convergence of monotone sequences, it is shown that the above ivp has a unique solution.

MSC:

39A12 Discrete version of topics in analysis
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
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References:

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