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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
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2020
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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
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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
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.
5
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.
6
Content available remote On some fundamental aspects of certain sum-difference equations
Pachpatte B. G.
Fasciculi Mathematici
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2009
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Nr 41
119-134
7
Content available remote Stability Analysis of Solutions to an Optimal Control Problem Associated With a Goursat-Darboux Problem
Idczak D., Majewski M., Walczak S.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 1
29-44
EN
In the present paper, some results concerning the continuous dependence of optimal solutions and optimal values on data for an optimal control problem associated with a Goursat-Darboux problem and an integral cost functional are derived.
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