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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 7
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Original Articles

Existence results for an impulsive neutral functional differential equation with state-dependent delay

A. Anguraj Department of Mathematics, PSG College of Arts and Science, Coimbatore -- 641 014, Tamil Nadu, India
,
M. Mallika Arjunan Department of Mathematics, PSG College of Arts and Science, Coimbatore -- 641 014, Tamil Nadu, India
&
Eduardo Hernández M Departamento de Matemática, ICMC, Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos SP, BrazilCorrespondence[email protected]
Pages 861-872 | Received 12 Jan 2007, Accepted 09 Mar 2007, Published online: 27 Sep 2007

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Mamadou Niang, Amadou Diop, Mohamed Didiya & Mamadou Abdoul Diop. (2022) Existence results of mild solutions for some stochastic integrodifferential equations with state-dependent delay and noninstantaneous impulses in Hilbert spaces. Research in Mathematics 9:1.
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Mouffak Benchohra, Johnny Henderson & Imene Medjadj. (2014) Global Existence Results for Functional Differential Inclusions with State-Dependent Delay. Mathematical Modelling and Analysis 19:4, pages 524-536.
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Mamadou Abdoul Diop, Khalil Ezzinbi & Modou Lo. (2014) Asymptotic stability of impulsive stochastic partial integrodifferential equations with delays. Stochastics 86:4, pages 696-706.
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Ravikumar Kasinathan, Ramkumar Kasinathan, Varshini Sandrasekaran & Juan J. Nieto. (2023) Qualitative Behaviour of Stochastic Integro-differential Equations with Random Impulses. Qualitative Theory of Dynamical Systems 22:2.
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A. Vinodkumar. (2023) Existence and uniqueness of solutions for random impulsive differential equation. Malaya Journal of Matematik 1:1, pages 8-13.
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Dumitru Baleanu, Ramkumar Kasinathan, Ravikumar Kasinathan & Varshini Sandrasekaran. (2023) Existence, uniqueness and Hyers-Ulam stability of random impulsive stochastic integro-differential equations with nonlocal conditions. AIMS Mathematics 8:2, pages 2556-2575.
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Amouria Hammou, Samira Hamani & Johnny Henderson. (2023) Impulsive fractional differential equations with state-dependent delay involving the Caputo-Hadamard derivative. Filomat 37:5, pages 1581-1590.
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A. Anguraj & A. Vinodkumar. (2023) Global existence and stability results for partial delay integro-differential equations with random impulses. Filomat 37:1, pages 317-334.
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Velusamy Kavitha, Mani Mallika Arjunan & Dumitru Baleanu. (2022) Non-instantaneous impulsive fractional-order delay differential systems with Mittag-Leffler kernel. AIMS Mathematics 7:5, pages 9353-9372.
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Shahram Rezapour, Hernán R. Henríquez, Velusamy Vijayakumar, Kottakkaran Sooppy Nisar & Anurag Shukla. (2021) A Note on Existence of Mild Solutions for Second-Order Neutral Integro-Differential Evolution Equations with State-Dependent Delay. Fractal and Fractional 5:3, pages 126.
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Venkatesh Usha, Dumitru BaleanuMani Mallika Arjunan. (2019) Existence results for an impulsive neutral integro-differential equations in Banach spaces. Analele Universitatii "Ovidius" Constanta - Seria Matematica 27:3, pages 231-257.
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E. Alaidarous, M. Benchohra & I. Medjadj. (2019) Global Existence Results for Neutral Functional Differential Inclusions with State-Dependent Delay. Ukrainian Mathematical Journal 70:11, pages 1661-1676.
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Mouffak Benchohra & Imene Medjadj. (2016) Measure of Noncompactness and Partial Functional Differential Equations with State-Dependent Delay. Differential Equations and Dynamical Systems 26:1-3, pages 139-155.
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Sanjukta DAS, Dwijendra PANDEY & N. SUKAVANAM. (2016) Existence of solution and approximate controllability of a second-order neutral stochastic differential equation with state dependent delay. Acta Mathematica Scientia 36:5, pages 1509-1523.
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Arumugam Vinodkumar, Muthusamy Gowrisankar & Prathiban Mohankumar. (2016) Existence and Stability Results on Nonlinear Delay Integro-Differential Equations with Random Impulses. Kyungpook mathematical journal 56:2, pages 431-450.
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Alka Chadha & Dwijendra N. Pandey. (2016) Existence of a mild solution for an impulsive nonlocal non-autonomous neutral functional differential equation. ANNALI DELL'UNIVERSITA' DI FERRARA 62:1, pages 1-21.
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Dimplekumar Chalishajar, Kulandhivel Karthikeyan & Annamalai Anguraj. (2016) Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces. Mathematics 4:2, pages 23.
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Sanjukta Das, Dwijendra N. Pandey & N. Sukavanam. (2014) Approximate Controllability of a Second Order Neutral Differential Equation with State Dependent Delay. Differential Equations and Dynamical Systems 24:2, pages 201-214.
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Mouffak Benchohra & Imene Medjadj. (2014) Global Existence Results for Neutral Functional Differential Equations with State-Dependent Delay. Differential Equations and Dynamical Systems 24:2, pages 189-200.
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Mamadou Abdoul Diop, Khalil Ezzinbi & Mahamat Mahamat Zene. (2015) Existence and stability results for a partial impulsive stochastic integro-differential equation with infinite delay. SeMA Journal 73:1, pages 17-30.
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Selvaraj Suganya, Dumitru Baleanu, Siva Selvarasu & Mani Mallika Arjunan. (2016) About the Existence Results of Fractional Neutral Integrodifferential Inclusions with State-Dependent Delay in Fréchet Spaces. Journal of Function Spaces 2016, pages 1-9.
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A. Vinodkumar, M. Gowrisankar & P. Mohankumar. (2015) Existence, uniqueness and stability of random impulsive neutral partial differential equations. Journal of the Egyptian Mathematical Society 23:1, pages 31-36.
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Abdelouaheb Ardjouni & Ahcene Djoudi. (2013) Existence, uniqueness and positivity of solutions for a neutral nonlinear periodic differential equation. Computational and Applied Mathematics 34:1, pages 17-27.
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Sanjukta Das, Dwijendra N. Pandey & N. Sukavanam. (2014) Existence of Solution and Approximate Controllability for Neutral Differential Equation with State Dependent Delay. International Journal of Partial Differential Equations 2014, pages 1-12.
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M. GOWRISANKAR, P. MOHANKUMAR & A. VINODKUMAR. (2014) Stability results of random impulsive semilinear differential equations. Acta Mathematica Scientia 34:4, pages 1055-1071.
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Zuomao Yan & Xiumei Jia. (2013) Impulsive Problems for Fractional Partial Neutral Functional Integro-Differential Inclusions with Infinite Delay and Analytic Resolvent Operators. Mediterranean Journal of Mathematics 11:2, pages 393-428.
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P. Muthukumar & C. Rajivganthi. (2013) Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. Journal of Control Theory and Applications 11:3, pages 351-358.
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Zuomao Yan & Xingxue Yan. (2012) Existence of solutions for impulsive partial stochastic neutral integrodifferential equations with state-dependent delay. Collectanea Mathematica 64:2, pages 235-250.
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M.C. Ranjini & A. Anguraj. (2013) Nonlocal impulsive fractional semilinear differential equations with almost sectorial operators. Malaya Journal of Matematik 1:02, pages 43-53.
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Ferenc Hartung. (2011) On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays. Annali di Matematica Pura ed Applicata 192:1, pages 17-47.
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N.Y. Nadaf & M. Mallika Arjunan. (2013) Existence and controllability results for damped second order impulsive neutral functional differential systems with state-dependent delay in Banach spaces. Malaya Journal of Matematik 1:1, pages 70-85.
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Mouffak Benchohra, Imene Medjadj, Juan J. Nieto & P. Prakash. (2013) Global Existence for Functional Differential Equations with State-Dependent Delay. Journal of Function Spaces and Applications 2013, pages 1-7.
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C. Ravichandran & J. J. Trujillo. (2013) Controllability of Impulsive Fractional Functional Integro-Differential Equations in Banach Spaces. Journal of Function Spaces and Applications 2013, pages 1-8.
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Velusamy Kavitha, Peng-Zhen Wang & R. Murugesu. (2012) Existence results for neutral functional fractional differential equations with state dependent-delay. Malaya Journal of Matematik 1:1, pages 50-61.
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Zhijian Yao. (2012) Existence and Nonexistence of Positive Periodic Solution for Impulsive Nicholson's Blowflies Model. AASRI Procedia 1, pages 365-370.
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Ganesan Arthi & Krishnan Balachandran. (2011) CONTROLLABILITY OF SECOND-ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY. Bulletin of the Korean Mathematical Society 48:6, pages 1271-1290.
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Junxia Wang. (2011) Existence and stability of solutions for neutral differential equations with delay. Existence and stability of solutions for neutral differential equations with delay.
Hernán R. Henríquez, Bruno De Andrade & Marcos Rabelo. (2011) Existence of Almost Periodic Solutions for a Class of Abstract Impulsive Differential Equations. ISRN Mathematical Analysis 2011, pages 1-21.
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Zuomao Yan. (2011) Existence of solutions for nonlocal impulsive partial functional integrodifferential equations via fractional operators. Journal of Computational and Applied Mathematics 235:8, pages 2252-2262.
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A. Anguraj, Shujin Wu & A. Vinodkumar. (2011) The existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness. Nonlinear Analysis: Theory, Methods & Applications 74:2, pages 331-342.
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Y.-K. Chang, Juan J. Nieto & Zhi-Han Zhao. (2010) Existence results for a nondensely-defined impulsive neutral differential equation with state-dependent delay. Nonlinear Analysis: Hybrid Systems 4:3, pages 593-599.
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A. Anguraj & A. Vinodkumar. (2010) Existence, uniqueness and stability results of random impulsive semilinear differential systems. Nonlinear Analysis: Hybrid Systems 4:3, pages 475-483.
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Claudio Cuevas, Gaston M. N’Guérékata & Marcos Rabelo. (2010) Mild solutions for impulsive neutral functional differential equations with state-dependent delay. Semigroup Forum 80:3, pages 375-390.
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Y. K. Chang & W. S. Li. (2009) Solvability for Impulsive Neutral Integro-Differential Equations with State-Dependent Delay via Fractional Operators. Journal of Optimization Theory and Applications 144:3, pages 445-459.
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Yong-Kui Chang, A. Anguraj & K. Karthikeyan. (2009) Existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators. Nonlinear Analysis: Theory, Methods & Applications 71:10, pages 4377-4386.
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Wen-Sheng Li, Yong-Kui Chang & Juan J. Nieto. (2009) Solvability of impulsive neutral evolution differential inclusions with state-dependent delay. Mathematical and Computer Modelling 49:9-10, pages 1920-1927.
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