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A Contribution to the Study of Functional Differential Equations with Impulses

2000; Wiley; Volume: 218; Issue: 1 Linguagem: Inglês

10.1002/1522-2616(200010)218

1522-2616

Daniel Franco, Eduardo Liz, Juan J. Nieto, Yuri V. Rogovchenko,

Fractional Differential Equations Solutions

Mathematische NachrichtenVolume 218, Issue 1 p. 49-60 Original Paper A Contribution to the Study of Functional Differential Equations with Impulses Daniel Franco, Daniel Franco Departamento de Matemática Aplicada I, E. T. S. I. Industriales, Universidad Nacional de Educación a Distancia, Madrid, SpainSearch for more papers by this authorEduardo Liz, Eduardo Liz Departamento de Matemática Aplicada, E. T. S. I. Telecomunicación, Universidad de Vigo, SpainSearch for more papers by this authorJuan J. Nieto, Juan J. Nieto Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, SpainSearch for more papers by this authorYuri V. Rogovchenko, Yuri V. Rogovchenko Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, TurkeySearch for more papers by this author Daniel Franco, Daniel Franco Departamento de Matemática Aplicada I, E. T. S. I. Industriales, Universidad Nacional de Educación a Distancia, Madrid, SpainSearch for more papers by this authorEduardo Liz, Eduardo Liz Departamento de Matemática Aplicada, E. T. S. I. Telecomunicación, Universidad de Vigo, SpainSearch for more papers by this authorJuan J. Nieto, Juan J. Nieto Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, SpainSearch for more papers by this authorYuri V. Rogovchenko, Yuri V. Rogovchenko Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, TurkeySearch for more papers by this author First published: 22 September 2000 https://doi.org/10.1002/1522-2616(200010)218:1 3.0.CO;2-6Citations: 34AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract A periodic boundary value problem for a special type of functional differential equations with impulses at fixed moments is studied. A comparison result is presented that allows to construct a sequence of approximate solutions and to give an existence result. Several particular cases are considered. References [1] Ballinger, G., and Liu, X.: Permanence of Population Growth Models with Impulsive Effects, Math. Comput. Modelling 26 (1997), 59–72 10.1016/S0895-7177(97)00240-9 Web of Science®Google Scholar [2] Blaquiere, A.: Differential Games with Piecewise Continuous Trajectories, Lecture Notes in Control and Informat. Sci. 3 (1977), 34–69, Springer–Verlag, New York 10.1007/BFb0009063 Google Scholar [3] Case, J.: Impulsively Controlled D. G. . In: J. D. Grote (Ed.), The Theory and Application of Differential Games, D. Reidel Publishing Co., Dordrecht–Boston, Mass., 1975 Google Scholar [4] Domoshnitsky, A., and Drakhlin, M.: Nonoscillation of First Order Impulse Differential Equations with Delay, J. Math. Anal. Appl. 206 (1997), 254–269 10.1006/jmaa.1997.5231 Web of Science®Google Scholar [5] Glass, L., and Mackey, M.C.: Oscillations and Chaos in Physiological Control Systems, Science 197 (1977), 287–289 10.1126/science.267326 PubMedWeb of Science®Google Scholar [6] Glass, L., and Mackey, M.C.: Pathological Conditions Resulting from Instabilities in Physiological Control Systems, Ann. N. Y. Acad. Sci. 316 (1979), 214–235 10.1111/j.1749-6632.1979.tb29471.x CASPubMedGoogle Scholar [7] Hale, J.K.: Theory of Functional Differential Equations (2nd ed.), Springer–Verlag, New York, 1977 Google Scholar [8] Hale, J.K., and Verduyn Lunel, S.M.: Introduction to Functional Differential Equations, Springer–Verlag, New York, 1993 Google Scholar [9] Hristova, S.G., and Bainov, D.D.: Monotone Iterative Techniques of V. Lakshmikanthamfor a Boundary Value Problem for Systems of Impulsive Differential Equations with “supremum”, J. Math. Anal. Appl. 172 (1993), 339–352 10.1006/jmaa.1993.1028 Web of Science®Google Scholar [10] Kirane, M., and Rogovchenko, Yu.V.: Comparison Results for Systems of Impulse Parabolic Equations with Applications to Population Dynamics, Nonlinear Anal. 28 (1997), 263–277 10.1016/0362-546X(95)00159-S Web of Science®Google Scholar [11] Kolmanovskii, V., and Myshkis, A.: Applied Theory of Functional Differential Equations, Kluwer Acad. Pub., London, 1992. Google Scholar [12] Ladde, G.S., Lakshmikantham, V., and Vatsala, A.S.: Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985 Google Scholar [13] Lakshmikantham, V., Bainov, D.D., and Simeonov, P.S.: Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989 Google Scholar [14] Leszcynski, H.: Existence of Solutions of Impulsive Functional–Differential Systems, Nonlinear Anal. 28 (1997), 1709–1717 Google Scholar [15] Liu, X.: Iterative Methods for Solutions of Impulsive Functional–Differential Systems, Appl. Anal. 44 (1992), 171–182 10.1080/00036819208840076 Google Scholar [16] Liu, X., and Willms, A.: Impulsive Stabilizability of Autonomous Systems, J. Math. Anal. Appl. 187 (1994), 17–39 10.1006/jmaa.1994.1342 Web of Science®Google Scholar [17] Liz, E.: Abstract Monotone Iterative Technique and Applications to Impulsive Differential Equations, Dynam. Contin. Discrete Impuls. Systems 3 (1997), 443–452 Web of Science®Google Scholar [18] Murray, J.D.: Mathematical Biology, 2nd edn., Springer–Verlag, New York, 1993 Google Scholar [19] Myshkis, A.D.: Vibrations of the String with Energy Dissipation and Impulsive Feedback Support, Nonlinear Anal. 26 (1996), 1271–1278 10.1016/0362-546X(94)00339-J Web of Science®Google Scholar [20] Nieto, J.J.: An Abstract Monotone Iterative Technique, Nonlinear Anal. 28 (1997), 1923–1933 10.1016/S0362-546X(97)89710-6 Web of Science®Google Scholar [21] Samoilenko, A.M., and Perestyuk, N.A.: Impulsive Differential Equations, World Scientific, Singapore, 1995 Google Scholar [22] Xu, H.K., and Liz, E.: Boundary Value Problems for Differential Equations with Maxima, Nonlinear Stud. 3 (1996), 231–241 Google Scholar Citing Literature Volume218, Issue1October 2000Pages 49-60 ReferencesRelatedInformation