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Oscillations in systems of impulsive nonlinear partial differential equations with distributed deviating arguments

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Języki publikacji
EN
Abstrakty
EN
In this paper, we consider systems of impulsive nonlinear neutral delay partial differential equations with distributed deviating arguments and sufficient conditions for the oscillation of the system under the Dirichlet boundary condition. The main results are illustrated by one example.
Rocznik
Tom
Strony
13--33
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
  • Department of Mathematics Universidade Federal de Santa Catarina Florianópolis, Brazil 88040-100
  • Department of Electrical and Electronic Engineering Educators School of Pedagogical and Technological Education (aspete) 14121, Athens, Greece
autor
  • PG and Research Department of Mathematics Thiruvalluvar Government Arts College (Affiliated to Periyar University, Salem - 636 011) Rasipuram - 637 401, Namakkal (Dt), Tamil Nadu, India
autor
  • Department of Mathematics Mahendra College of Engineering (Affiliated to Anna University, Chennai.) Minnapalli, Salem - 636106
  • PG and Research Department of Mathematics Thiruvalluvar Government Arts College (Affiliated to Periyar University, Salem - 636 011) Rasipuram - 637 401, Namakkal (Dt), Tamil Nadu, India
Bibliografia
  • [1] Agarwal R.P., Meng F.N., Li W.N., Oscillation of solutions of systems of neutral type partial functional differential equations, Computers and Mathematics with Applications, 44(5-6)(2002), 777-786.
  • [2] Bainov D.D., Mishev D.P., Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, New York, 1991.
  • [3] Cui B.T., Liu Y., Deng F., Some oscillation problems for impulsive hyperbolic differential systems with several delays, Appl. Math. Comput., 146(2-3)(2003), 667-679.
  • [4] Du L., Fu W., Fan M., Oscillatory solutions of delay hyperbolic system with distributed deviating arguments, Appl. Math. Comput., 154(2)(2004), 521-529.
  • [5] Erbe L.H., Freedman H.I., Liu X.Z., Wu J.H., Comparison principles for impulsive parabolic equations with applications to models of single species growth, J. Aust. Math. Soc., 32(4)(1991), 382-400.
  • [6] Fu X.L., Liu X., Oscillation criteria for impulsive hyperbolic systems dynamics of continuous, Discrete Impul. Syst., 3(1999), 225-244.
  • [7] Gopalsamy K., Zhang B.G., On delay differential equations with impulses, J. Math. Anal. Appl., 139(1)(1989), 110-122.
  • [8] Hardy G.H., Littlewood J.E., Pólya G., Inequalities, Cambridge University Press, Cambridge, UK, 1988.
  • [9] Ladde G.S., Lakshmikantham V., Zhang B.G., Oscillation Theory of Differential Equations with Deviating Arguments, Marcl Dekker, Inc, New York, 1987.
  • [10] Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory of Impulsive Differential Equations, World Scientific Publishers, Singapore, 1989.
  • [11] Li Y.K., Oscillation of systems of hyperbolic differential equations with deviating arguments, Acta Math. Sinica, 40(1997), 100-105, (in Chinese).
  • [12] Li W.N., On the forced oscillation of solutions for systems of impulsive parabolic differential equations with several delays, J. Comput. Appl. Math., 181(2005), 46-57.
  • [13] Li W.N., Cui B.T., Oscillation for systems of neutral delay hyperbolic differential equations, Indian J. Pure Appl. Math., 31(8)(2000), 933-948.
  • [14] Li W.N., Cui B.T., Debnath L., Oscillation of systems of certain neutral delay parabolic differential equations, Journal of Applied Mathematics and Stochastic Analysis, 16(1)(2003), 83-94.
  • [15] Li W.N., Debnath L., Oscillation of a systems of delay hyperbolic differential equations, Int. J. Appl. Math., 2(2000), 417-431.
  • [16] Li W.N., Meng F., On the forced oscillation of systems of neutral parabolic differential equations with deviating arguments, J. Math. Anal. Appl., 288(1)(2003), 20-27.
  • [17] Lin W.X., Some oscillation theorems for systems of partial equations with deviating arguments, Journal of Biomathematics, 18(4)(2003), 400-407.
  • [18] Liu G., Wang C., Forced oscillation of neutral impulsive parabolic partial differential equations with continuous distributed deviating arguments, Open Access Library Journal, 1(2014), 1-8.
  • [19] Mil’Man V.D., Myshkis A.D., On the stability of motion in the presence of impulse, Siberian Math. J., 1(2)(1960), 233-237.
  • [20] Philos Ch.G., A new criterion for the oscillatory and asymptotic behavior of delay differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math., 39(1981), 61-64.
  • [21] Sadhasivam V., Kavitha J., Raja T., Forced oscillation of nonlinear impulsive hyperbolic partial differential equation with several delays, Journal of Applied Mathematics and Physics, 3(2015), 1491-1505.
  • [22] Sadhasivam V., Kavitha J., Raja T., Forced oscillation of impulsive neutral hyperbolic differential equations, International Journal of Applied Engineering Research, 11(1)(2016), 58-63.
  • [23] Sadhasivam V., Raja T., Kalaimani T., Oscillation of nonlinear impulsive neutral functional hyperbolic equations with damping, International Journal of Pure and Applied Mathematics, 106(8)(2016), 187-197.
  • [24] Sadhasivam V., Raja T., Kalaimani T., Oscillation of impulsive neutral hyperbolic equations with continuous distributed deviating arguments, Global Journal of Pure and Applied Mathematics, 12(3)(2016), 163-167.
  • [25] Tao T., Yoshida N., Oscillation of nonlinear hyperbolic equations with distributed deviating arguments, Toyama Math. J., 28(2005), 27-40.
  • [26] Tao T., Yoshida N., Oscillation criteria for hyperbolic equations with distributed deviating arguments, Indian J. Pure Appl. Math., 37(5)(2006), 291-305.
  • [27] Vladimirov V.S., Equations of Mathematics Physics, Nauka, Moscow, 1981.
  • [28] Wang P.G., Wang M., Ge W., Further results on oscillation of hyperbolic differential equations of neutral type, Journal of Applied Analysis, 10(1)(2004), 117-129.
  • [29] Wang P.G., Zhao J., Ge W., Oscillation criteria of nonlinear hyperbolic equations with functional arguments, Comput. Math. Appl., 40(2000), 513-521.
  • [30] Wu J., Theory and Applications of Partial Functional Differential Eąuations, Springer-Verlag, New York, 1996.
  • [31] Yoshida N., Oscillation Theory of Partial Differential Equations, World Scientific, Singapore, 2008.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bb67c656-5789-4495-9cbd-36d13fe29bcc
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