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1
Content available remote Chandrasekhar quadratic and cubic integral equations via Volterra-Stieltjes quadratic integral equation
El-Sayed Ahmed M. A., Omar Yasmin M. Y.
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
25--36
EN
In this work, we study the existence of one and exactly one solution x ∈ C[0, 1], for a delay quadratic integral equation of Volterra-Stieltjes type. As special cases we study a delay quadratic integral equation of fractional order and a Chandrasekhar cubic integral equation.
2
Content available On the existence of continuous positive monotonic solutions of a self-reference quadratic integral equation
El-Sayed Ahmed M.A., Ebead Hanaa R.
Journal of Mathematics and Applications
|
2020
|
Vol. 43
67--80
EN
In this work we study the existence of positive monotonic solutions of a self-reference quadratic integral equation in the class of continuous real valued functions. The continuous dependence of the uniquesolution will be proved. Some examples will be given.
3
Content available remote A nonstandard Volterra integral equation on time scales
Reinfelds Andrejs, Christian Shraddha
Demonstratio Mathematica
|
2019
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Vol. 52, nr 1
503--510
EN
This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.
4
Content available Solutions of fractional nabla difference equations - existence and uniqueness
Jonnalagadda J. M.
Opuscula Mathematica
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2016
|
Vol. 36, no. 2
215--238
EN
In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.
5
Some theorems on fractional semilinear evolution equations
Tidke H. L.
Journal of Applied Analysis
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2012
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Vol. 18, nr 2
209-224
EN
In this paper, we investigate the existence, uniqueness and other properties of solutions of fractional semilinear evolution equations in Banach spaces. The results are obtained by using fractional calculus, the well-known Banach fixed point theorem coupled with Bielecki type norm and the integral inequality established by E. Hernandez.
6
On a nonlinear dynamic integrodifferential equation on time scales
Pachpatte D. B.
Journal of Applied Analysis
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2010
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Vol. 16, nr 2
279-294
EN
The main objective of the present paper is to study some basic qualitative properties of solutions of a certain nonlinear integrodifferential equation on time scales. The tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain inequality with explicit estimate on time scales.
7
Content available remote Existence and uniqueness of mild and strong solutions of nonlinear Volterra integrodifferential equations in Banach spaces
Tidke H. L., Dhakne M. B.
Demonstratio Mathematica
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2010
|
Vol. 43, nr 3
643-652
EN
In this paper we prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra integrodifferential equation with nonlocal condition. Our analysis is based on semigroup theory and Banach fixed point theorem and inequalities are established by Gronwall and B. G. Pachpatte.
8
Content available remote On some fundamental aspects of certain sum-difference equations
Pachpatte B. G.
Fasciculi Mathematici
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2009
|
Nr 41
119-134
9
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.
10
Content available remote On Volterra-Fredholm integral equation in two variables
Pachpatte B.
Demonstratio Mathematica
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2007
|
Vol. 40, nr 4
839-852
EN
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.
11
Content available remote Superlinear elliptic systems with distributed and boundary controls
Bors D.
Control and Cybernetics
|
2005
|
Vol. 34, no 4
987-1004
EN
The paper investigates the nonlinear partial differential equations of the superlinear elliptic type with the Dirichlet boundary data. Some sufficient conditions, under which the solutions of considered equations depend continuously on distributed and boundary controls, are proved. The proofs of the main results are based on variational methods.
12
On the problem of propagation of heat in mixtures
Lesan D., Quintanilla R.
Applied Mechanics and Engineering
|
1999
|
Vol. 4, no 3
529-551
EN
This paper is concerned with the linear theory of heat propagation in a binary mixture of rigid heat conductors. First, the equilibrium theory is studied. A solution of Galerkin type is established and fundamental solutions are derived. The potentials of single-layer and double-layer are used to reduce the boundary value problems to singular integral equations. Existence and uniqueness results are established. The second part of the paper is concerned with the dynamical theory. A continuous dependence result and a spatial decay estimate are derived.
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