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We consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. Although these problem classes are not in the focus of the main stream literature, they are interesting, not only in their own right, but also because they may arise from the analysis of certain classes of differential-algebraic systems of partial differential equations. In the first part of the paper, we deal with two-dimensional integral-algebraic equations. Next, we analyze Volterra integral...

Existence and upper semicontinuity of global attractors for neural fields in an unbounded domain.

da Silva, Severino Horacio (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of extremal solutions of a three-point boundary value problem for a general second order $p$ -Laplacian integro-differential equation.

Ahmad, Bashir, Alsaedi, Ahmed (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Existence of global solutions to nonlinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions.

Tidke, Haribhau L. (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of mild solutions to fractional integrodifferential equations of neutral type with infinite delay.

Li, Fang, Zhang, Jun (2011)

Advances in Difference Equations [electronic only]

Existence of nonnegative periodic solutions in neutral integro-differential equations with functional delay

Imene Soulahia, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)

Commentationes Mathematicae Universitatis Carolinae

The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay $x^{'} (t) = - \int_{t - τ (t)}^{t} a (t, s) g (x (s)) d s + \frac{d}{d t} Q (t, x (t - τ (t))) + G (t, x (t), x (t - τ (t))) .$ We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for $τ$ , $g$ , $a$ , $Q$ and $G$ to show that this sum of mappings fits into the framework of a modification of Krasnoselskii’s...

Existence of periodic solutions for first-order totally nonlinear neutral differential equations with variable delay

Abdelouaheb Ardjouni, Ahcène Djoudi (2014)

Commentationes Mathematicae Universitatis Carolinae

We use a modification of Krasnoselskii’s fixed point theorem due to Burton (see [Liapunov functionals, fixed points and stability by Krasnoselskii’s theorem, Nonlinear Stud. 9 (2002), 181–190], Theorem 3) to show that the totally nonlinear neutral differential equation with variable delay $x^{'} (t) = - a (t) h (x (t)) + c (t) x^{'} (t - g (t)) Q^{'} (x (t - g (t))) + G (t, x (t), x (t - g (t))),$ has a periodic solution. We invert this equation to construct a fixed point mapping expressed as a sum of two mappings such that one is compact and the other is a large contraction. We show that the mapping fits...

Existence of periodic solutions for integrodifferential impulsive periodic system on Banach space.

Wang, Jinrong, Xiang, X., Wei, W. (2008)

Abstract and Applied Analysis

Existence of positive solutions to some impulsive second-order integrodifferential equations.

Atmania, Rahima (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of solutions and controllability of nonlinear integro-differential systems in Banach spaces.

Balachandran, K., Park, J.Y. (2003)

Mathematical Problems in Engineering

Existence of solutions for a class of quasi-linear singular integro-differential equations in a Sobolev space.

Hassan, A.A.M., Amer, S.M. (2009)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Existence of Solutions for a Class of Quasi-Linear Singular Integro-Differential Equations

Hassan, A. A. M., Amer, S. M. (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 45F15, 45G10, 46B38.An existence theorem is proved for a class of quasi-linear singular integro-differential equations with Cauchy kernel.

Existence of solutions for a weighted $p (t)$ -Laplacian impulsive integrodifferential system with multipoint and integral boundary value conditions.

Dong, Rong, Guo, Yunrui, Zhao, Yuanzhang, Zhang, Qihu (2010)

Journal of Inequalities and Applications [electronic only]

Existence of solutions for abstract neutral integro-differential equations with unbounded delay

Eduardo M. Hernández, Donal O'Regan (2011)

Czechoslovak Mathematical Journal

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.

Existence of solutions for integrodifferential equations of fractional order with antiperiodic boundary conditions.

Alsaedi, Ahmed (2009)

International Journal of Differential Equations

Existence of Solutions for Integrodifferential Inclusions in Banach Spaces

Nikolaos S. Papageorgiou (1994)

Publications de l'Institut Mathématique

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