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Integral equation arising in the theory of partial differential equations

Pachpatte B. G.

Fasciculi Mathematici

2010

Nr 43

115-126

The aim of the present paper is to study some basic qualitative properties of solutions of a certain integral equation arising in the theory of partial differential equations. The well known Banach fixed point theorem and the new integral inequality with explicit estimate obtained in the present paper are used to establish the results.

Of neutral type hyperbolic integrodifferential equation

Pachpatte B. G.

Fasciculi Mathematici

2008

Nr 40

57-69

In this paper we study the existence, uniqueness and other properties of solutions of a certain neutral type hyperbolic integrodifferential equation in two independent variables. The Banach fixed point theorem and a certain integral inequality with explicit estimate are used to establish the results.

On higher order Volterra-Fredholm integrodifferential equation

Pachpatte B. G.

Fasciculi Mathematici

2007

Nr 37

35-48

In the present paper we study the existence, uniqueness and other properties of soltions of a certain higher order Volterra-Fredholm integrodifferential equation. The well known Banach fixed point theorem coupled with Bilecki type norm and the new integral inequality with explicit estimate are used to establish the results.

On Volterra-Fredholm integral equation in two variables

Pachpatte B.

Demonstratio Mathematica

2007

Vol. 40, nr 4

839-852

The aim of this paper is to study thexistence, uniqueness and other properties of solution of a certain Volterra-Fredholm integral equation in two independent variables. The main tools employed in the analysis are based on the applications of the well known Banach fixed point theorem and the new integral inequality with explicit estimate.