Existence results for a fractional equation with state-dependent delay.
dos Santos, José Paulo Carvalho, Cuevas, Claudio, de Andrade, Bruno (2011)
Advances in Difference Equations [electronic only]
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dos Santos, José Paulo Carvalho, Cuevas, Claudio, de Andrade, Bruno (2011)
Advances in Difference Equations [electronic only]
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Hernandez, E., Henriquez, H.R., Dos Santos, J.P.C. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Berezansky, Leonid, Diblík, Josef, Šmarda, Zdenĕk (2010)
Advances in Difference Equations [electronic only]
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Mouffak Benchohra, Benaouda Hedia (2010)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper we study the existence of solutions for impulsive differential equations with state dependent delay. Our results are based on the Leray–Schauder nonlinear alternative and Burton–Kirk fixed point theorem for the sum of two operators.
Bouzahir, Hassane (2007)
Journal of Inequalities and Applications [electronic only]
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Eduardo M. Hernández, Donal O'Regan (2011)
Czechoslovak Mathematical Journal
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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.
Balachandran, Krishnan, Kim, Jeong-Hoon, Leelamani, Arunachalam (2006)
Applied Mathematics E-Notes [electronic only]
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Marshal Anthoni, S., Kim, J.-H., Dauer, J.P. (2004)
International Journal of Mathematics and Mathematical Sciences
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Abdelouaheb Ardjouni, Ahcène Djoudi (2014)
Commentationes Mathematicae Universitatis Carolinae
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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 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...