Oscillation of Impulsive Hyperbolic Differential Equations with Distributed Delay
DOI:
https://doi.org/10.15613/sijrs/2017/v4i1/172389Keywords:
Distributed Delay, Impulse, Oscillation, Partial Differential Equations.Abstract
The present effort deals about oscillation of solutions of impulsive hyperbolic differential equations with distributed deviating arguments. Sufficient conditions are obtained for the oscillation of solutions using impulsive differential inequalities and integral averaging scheme with boundary condition. Example is provided to illustrate the obtained results.Downloads
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Bainov D, Minchev E. Estimates of solutions of impulsive parabolic equations and applications to the population dynamics. Publ Math. 1996; 40:85–94. Doi: https://doi.org/10.5565/ PUBLMAT_40196_06.
Baotong C, Lalli BS, Yuanhong Y. Forced oscillations of hyperbolic equations with deviating arguments. Acta Mathematicae Applicatae Sinica. 1995; 4:369–77.
Chan CY, Ke L, Remarks on impulsive quenching problems. Proc Dynam. Systems Appl. 1994; 1:59–62.
Deng L, Ge W, Wang PG. Oscillation of functional parabolic differential equations under the Robin boundary condition. Indian J Pure Appl Math. 2001; 32(4):509–14.
Du LL, Fu W, Fan MS. Oscillatory solutions of delay hyperbolic system with distributed deviating arguments. Appl Math Comput. 2004; 154:521–29. Doi: https://doi.org/10.1016/ S0096-3003(03)00732-X.
Erbe LH, Freedman HI, Liu XZ, Wu JH. Comparison principles for impulsive parabolic equations with applications to models of single species growth. J Austral Math Soc Ser. 1991; B32:382–400. Doi: https://doi.org/10.1017/ S033427000000850X.
Gao W, Wang J. Estimates of solutions of impulsive parabolic equations under Neumannboundary condition. J Math Anal Appl. 2003, 283:478–90. Doi: https://doi.org/10.1016/S0022247X(03)00275-0.
Liu Y, Zhang J, Yan J. Oscillation properties of higher order partial differential equations with distributed deviating arguments. Discrete Dyn Nat Soc. 2015; 2015:1–9. Doi: https:// doi.org/10.1155/2015/206261
Luo LP, Gao ZH, Ouyang ZG. Oscillation of nonlinear neutral parabolic partial differential equations with continuous distributed delay. Math Appl. 2006; 19:651–55.
Sadhasivam V, Raja T, Kalaimani T. Oscillation of nonlinear impulsive neutral functional hyperbolic equations with damping. International Journal of Pure and Applied Mathematics. 2016; 106(8):187–197.
Sadhasivam V, Raja T, Kalaimani T. Oscillation of impulsive neutral hyperbolic equations with continuous distributed deviating arguments, Global Journal of Pure and Applied Mathematics. 2016; 12(3):163–167.
Shoukaku Y. Forced oscillatory result of hyperbolic equations with continuous distributed deviating Arguments. Appl Math Lett. 2011; 24:407–411. Doi: https://doi.org/10.1016/j.aml.2010.10.012
Tanaka S, Yoshida N. Forced oscillation of certain hyperbolic equations with continuous distributed deviating arguments. Ann Polon Math. 2005; 85:37–54. Doi: https:// doi.org/10.4064/ap85-1-4
Vladimirov VS. Equations of mathematical physics. Moscow: Nauka; 1981.
Wang PG. Oscillatory criteria of nonlinear hyperbolic equations with continuous deviating arguments. Appl Math Comput. 1999; 106:163–169. Doi: https://doi.org/10.1016/ S0096-3003(98)10110-8
Wang PG, Wu Y, Caccetta L. Forced oscillation of a class of neutral hyperbolic differential equations. J Comput Appl Math. 2005; 177:301–308. Doi: https://doi.org/10.1016/j.cam.2004.09.021
Wang PG, Zhao J, Ge W. Oscillation criteria of nonlinear hyperbolic equations with functional arguments. Comput Math Appl. 2000; 40:513–21. Doi: https://doi.org/10.1016/ S0898-1221(00)00176-0
Wu JH. Theory and applications of partial functional differential equations. New York: Springer; 1996. Doi: https://doi.org/10.1007/978-1-4612-4050-1
Yoshida N. Oscillation theory of partial differential equations.Singapore: World Scientific; 2008. Doi: https://doi.org/10.1142/7046