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Forced Oscillation of Neutral Impulsive Parabolic Partial Differential Equations with Continuous Distributed Deviating Arguments

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DOI: 10.4236/oalib.1101168    1,334 Downloads   1,581 Views   Citations

ABSTRACT

This paper investigated oscillatory properties of solutions for nonlinear parabolic equations with impulsive effects under two different boundary conditions. By using integral averaging method, variable substitution and functional differential inequalities, we established several sufficient conditions. At last, we provided two examples to illustrate the results.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Liu, G. and Wang, C. (2014) Forced Oscillation of Neutral Impulsive Parabolic Partial Differential Equations with Continuous Distributed Deviating Arguments. Open Access Library Journal, 1, 1-8. doi: 10.4236/oalib.1101168.

References

[1] Yoshida, N. (1986) Oscillation of Nonlinear Parabolic Equations with Functional Arguments. Hiroshima Mathematical Journal, 16, 305-314.
[2] Minchev, P.E. and Bainov, D.D. (1988) Oscillation of the Solutions of Parabolic Differential Equations of Neutral Type. Applied Mathematics and Computation, 28, 97-111.
http://dx.doi.org/10.1016/0096-3003(88)90089-6
[3] Liu, A.P., Yu, W.H. and Ding, Y.H. (2001) Necessary and Sufficient Conditions for Oscillations of Nonlinear Parabolic Partial Differential Equations. Pure and Applied Mathematics, 18, 86-89.
[4] Yang, Q.G. (2004) Oscillations of Solutions of a Class of Nonlinear Neutral Partial Differential Equations. Indian Journal of Pure & Applied Mathematics, 35, 3-22.
[5] Shoukaku, Y. and Yoshida, N. (2010) Oscillations of Nonlinear Hyperbolic Equations with Functional Arguments via Riccati Method. Applied Mathematics and Computation, 217, 143-151.
http://dx.doi.org/10.1016/j.amc.2010.05.030
[6] Lakshmikantham, V., Bainov, D.D. and Simeonov, P.S. (1989) Impulsive Differential Inequalities. In: Lakshmikantham, V., Bainov, D.D. and Simeonov, P.S., Eds., Theory of Impulsive Differential Equations, World Scientific Publishing Co. Pte. Ltd., Singapore City, 32-35.
[7] Erbe, L., Freedman, H., Liu, X.Z. and Wu, J.H. (1991) Comparison Principles for Impulsive Parabolic Equations with Application to Models of Single Species Growth. Journal of the Australian Mathematical Society, 32, 382-400.
http://dx.doi.org/10.1017/S033427000000850X
[8] Bainov, D.D. and Minchev, P.E. (1998) Forced Oscillations of Solutions of Impulsive Nonlinear Parabolic Differential-Difference Equations. Journal of the Korean Mathematical Society, 35, 881-890.
[9] Bainov, D.D. and Minchev, P.E. (1996) Oscillation of Solutions of Impulsive Nonlinear Parabolic Differential-Difference Equations. International Journal of Theoretical Physics, 35, 207-215.
http://dx.doi.org/10.1007/BF02082944
[10] Fu, X.L., Liu, X.Z. and Sivaloganathan, S. (2002) Oscillation Criteria for Impulsive Parabolic Differential Equations with Delay. Journal of Mathematical Analysis and Applications, 268, 647-664.
http://dx.doi.org/10.1006/jmaa.2001.7840
[11] Liu, A.P., Xiao, L. and He, M.X. (2004) Oscillation of Nonlinear Hyperbolic Differential Equations with Impulses. Nonlinear Oscillations, 7, 425-431.
http://dx.doi.org/10.1007/s11072-005-0022-x
[12] Liu, A.P., Ma, Q.X. and He, M.X. (2006) Oscillation of Nonlinear Impulsive Parabolic Equations of Neutral Type. Rocky Mountain Journal of Mathematics, 36, 1011-1026.
http://dx.doi.org/10.1216/rmjm/1181069442
[13] Tanaka, S. and Yoshida, N. (2005) Forced Oscillation of Certain Hyperbolic Equations with Continuous Distributed Deviating Arguments. Annales Polonici Mathematici, 85, 37-54.
http://dx.doi.org/10.4064/ap85-1-4
[14] Luo, L.P., Gao, Z.H. and Ouyang, Z.G. (2006) Oscillation of Nonlinear Neutral Parabolic Partial Functional Differential Equations with Continuous Distribution Delay. Mathematica Applicata, 19, 651-655.
[15] Shoukaku, Y. (2011) Forced Oscillatory Result of Hyperbolic Equations with Continuous Distributed Deviating Arguments. Applied Mathematics Letters, 24, 407-411.
http://dx.doi.org/10.1016/j.aml.2010.10.012
[16] Yan, J.R. and Kou, C.H. (2001) Oscillation of Solutions of Impulsive Delay Differential Equations. Journal of Mathematical Analysis and Applications, 254, 358-370.
http://dx.doi.org/10.1006/jmaa.2000.7112
[17] Deng, L.H. and Ge, W.G. (2001) Oscillation of the Solutions of Parabolic Equations with Impulses. Acta Mathematica Sinica, 44, 501-506.
[18] Yan, J.R. (2004) Oscillation Properties of Solutions for Impulsive Delay Parabolic Equations. Acta Mathematica Sinica, 47, 579-586.
[19] Liu, A.P., Liu, T. and Zou, M. (2011) Oscillation of Nonlinear Impulsive Parabolic Differential Equations of Neutral Type. Rocky Mountain Journal of Mathematics, 41, 833-850.
http://dx.doi.org/10.1216/RMJ-2011-41-3-833

  
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