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Initial value problem for first-order integro-differential equation of Volterra type on time scales. (English) Zbl 1065.45005
The authors combine the monotone iterative technique with fixed point theory to prove the existence of extremal solutions to the following integro-differential equation \[ x^{\Delta}=f\left(t,x,\int_{0}^{t}k(t,s)x(s)\Delta s\right), \quad t\in J:=[0,a] \]
\[ x(0)=0, \] where \(f:J\times \mathbb R\times \mathbb R\to \mathbb R\) and \(k: J\times J\to \mathbb R.\)

MSC:
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
45L05 Theoretical approximation of solutions to integral equations
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