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Approximate solutions for integrodifferential equations of the neutral type

B. G. Pachpatte — 2010

Commentationes Mathematicae Universitatis Carolinae

The main objective of the present paper is to study the approximate solutions for integrodifferential equations of the neutral type with given initial condition. A variant of a certain fundamental integral inequality with explicit estimate is used to establish the results. The discrete analogues of the main results are also given.

Approximation of solutions of a difference-differential equation

B. G. Pachpatte — 2010

Archivum Mathematicum

In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results. Applications to a Volterra type difference-integral equation are also given.

On a parabolic integrodifferential equation of Barbashin type

B. G. Pachpatte — 2011

Commentationes Mathematicae Universitatis Carolinae

In the present paper we study some basic qualitative properties of solutions of a nonlinear parabolic integrodifferential equation of Barbashin type which occurs frequently in applications. The fundamental integral inequality with explicit estimate is used to establish the results.

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