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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.

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.

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