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1
Content available remote Integral equation arising in the theory of partial differential equations
Pachpatte B. G.
Fasciculi Mathematici
|
2010
|
Nr 43
115-126
EN
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.
2
Content available remote Approximate solutions of a certain second order integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
|
2010
|
Nr 45
99-109
EN
The main aim of this paper is to study the approximate solutions of a certain second order Volterra type integrodifferential equation with given initial values. A variant of a certain basic integral inequality with explicit estimate is used to establish the results.
3
Content available remote On some fundamental aspects of certain sum-difference equations
Pachpatte B. G.
Fasciculi Mathematici
|
2009
|
Nr 41
119-134
4
Content available remote Growth estimates on mixed Volterra-Fredholm type integral inequalities
Pachpatte B. G.
Fasciculi Mathematici
|
2009
|
Nr 42
63-72
EN
In this paper we establish explicit estimates on some mixed Volterra-Fredholm type integral inequalities which can be used as tools in certain applications. Some applications are also given to illustrate the usefulness of the results.
5
Content available remote On integrated Volterra integrodifferential equation of higher order
Pachpatte B. G.
Fasciculi Mathematici
|
2008
|
Nr 39
47-61
EN
In this paper we study the existence and other properties of solutions of a certain iterated Volterra integrodifferential equation of higher order. The tools employed in the analysis are based on application of the Leray-Schauder alternative and a certain integral inequality which provides explicit bound on the unknown function.
6
Content available remote Of neutral type hyperbolic integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
|
2008
|
Nr 40
57-69
EN
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.
7
Content available remote On higher order Volterra-Fredholm integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
|
2007
|
Nr 37
35-48
EN
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.
8
Content available remote New inequalities of Ostrowski-Grüss type
Pachpatte B. G.
Fasciculi Mathematici
|
2007
|
Nr 38
97-104
EN
The main aim of the present paper is to establish new inequalities of Ostrowski-Griiss type, involving two functions and their derivatives via certain integral identity.
9
Content available remote Explicit bounds on some retarded integral inequalities
Pachpatte B. G.
Fasciculi Mathematici
|
2005
|
Nr 35
85-98
EN
In this paper we establish some new retarded integral inequalities which provide explicit bounds on unknown functions. Applications are also given to illustrate the usefulness of one of our results.
10
Content available remote On some basic finite difference inequalities
Pachpatte B. G.
Fasciculi Mathematici
|
2004
|
Nr 34
65-71
EN
In this paper we establish some basic finite difference inequalities which can be used as tools in the study of qualitative properties of the solutions of finite difference equations and numerical analysis.
11
Content available remote Inequalities useful in the theory of certain partial differential equations
Pachpatte B. G.
Fasciculi Mathematici
|
2002
|
Nr 33
49-56
EN
In this paper we establish some new integral inequalities in two independent variables which can be used as tools in the theory of certain classes of hyperbolic partial differential equations. The analysis used in the proofs is elementry and the results established provide new estimates on these types of inequalities.
12
Content available remote On certain integral inequalities and their discrete analogues
Pachpatte B. G.
Demonstratio Mathematica
|
2002
|
Vol. 35, nr 2
243-250
13
Content available remote Integral inequalities of Wirtinger and Opial type in three independent variables
Pachpatte B. G.
Fasciculi Mathematici
|
1999
|
Nr 30
113-129
EN
In the present paper we establish some new Wirtinger and Opial type integral inequalities involving functions of three independent variables and their partial derivatives. The method used in the proof is elementary and our results provide new estimates on inequalities ofthis type.
14
Content available remote Integral inequalities associated to the zeros of solutions of certain higher order differential equations
Pachpatte B. G.
Fasciculi Mathematici
|
1999
|
Nr 29
87-97
EN
The aim of the present paper os to establish some new integra1 inequalities associated to the zeros of the solutions of certain higher order differential equations by using elementary analysis. The inequalities obtained here can be effectively used in the study of qualitative behavior of solutions of the corresponding equations.
15
Content available remote A note on multivariate variants of Hardy's inequality
Pachpatte B. G.
Fasciculi Mathematici
|
1999
|
Nr 30
107-112
EN
In the present note we establish multivariate generalizations of the certain variants ofthe well known Hardy's inequality. Our results are obtained by using the well known Fubini's theorem.
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