International Journal of Modern Science and Technology
International Journal of Modern Science and Technology, Vol. 2, No. 4, 2017, Pages 158-167.
Grey Scale Histogram Based Image Segmentation Using Firefly Algorithm
V. Sadhasivam, T. Kalaimani, T. Raja
PG and Research Department of Mathematics, Thiruvalluvar Government Arts College, Rasipuram - 637 401. India.
*Corresponding author’s e-mail: firstname.lastname@example.org
The present work considered a class of boundary value problems associated with even order impulsive neutral partial functional differential equations with continuous distributed deviating arguments and damping term. Necessary and Sufficient conditions are obtained for the oscillation of solutions using impulsive differential inequalities and integral averaging scheme with Robin boundary condition. Examples are specified to illustrate the important results. .
Keywords: Neutral partial differential equations; Oscillation; Impulse; Distributed deviating arguments.
- Sturm C. Surles quations diff rentielles lin aries du second ordre. J Math Pure Appl. 1836;1:106-186.
- Hartman P, Wintner A. On a comaparison theorem for self-adjoint partial differential equations of elliptic type. Proc Amer Math Soc. 1955;6:862-865.
- Gopalsamy K, Zhang BG. On delay differential equations with impulses. J Math Anal Appl. 1989;139:110-122.
- Lakshmikantham V, Bainov DD, Simeonov V. Theory of Impulsive Differential Equations, World Scientific Publishers, Singapore, 1989.
- Erbe L, Freedman H, Liu XZ, Wu JH. Comparison principles for impulsive parabolic equations with application to models of single species growth. J Aust Math Soc. 1991;32:382-400.
- Bainov DD, Mishev DP. Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, New York, 1991.
- Judith JEJO, Okelo NB, Kiogora R, Onyango T. Numerical solutions of mathematical model on effects of biological control on cereal aphid population dynamics. Int J Mod Sci Technol. 2016;1(4):138-143.
- Judith JEJO, Okelo NB, Kiogora R, Onyango T. Construction and qualitative analysis of mathematical model for biological control on cereal aphid population dynamics. Int J Mod Sci Technol. 2016;1(5):150-158.
- Ladde GS, Lakshmikantham V, Zhang BG. Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, Inc, New York, 1987.
- Wu JH. Theory and Applications of Partial Functional Differential Equations, Springer, New York, 1996.
- Liu GJ, Wang CY. Forced oscillation of neutral impulsive parabolic partial differential equations with continuous distributed deviating arguments, Open Access Library Journal, 2014;1:1-8.
- Sadhasivam V, Kavitha J, Raja T. Forced oscillation of nonlinear impulsive hyperbolic partial differential equation with several delays. Journal of Applied Mathematics and Physics. 2015;3:1491-1505.
- Sadhasivam V, Kavitha J, Raja T. Forced oscillation of impulsive neutral hyperbolic differential equations. International Journal of Applied Engineering Research. 2016;11(1):58-63.
- 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.
- Tanaka S, Yoshida N. Forced oscillation of certain hyperbolic equations with continuous distributed deviating arguments. Ann Polon Math. 2005;85:37-54.
- Thandapani E, Savithri R. On oscillation of a neutral partial functional differential equations. Bull Inst Math Acad Sin. 2003;31(4):273-292.
- Yoshida N. Oscillation Theory of Partial Differential Equations, World Scientific, Singapore, 2008.
- Gui G, Xu Z. Oscillation of even order partial differential equations with distributed deviating arguments. J Comput Appl Math. 2009;228:20-29.
- Li WN, Debnath L. Oscillation of higher-order neutral partial functional differential equations. Appl Math Lett. 2003;16:525-530.
- Li WN, Sheng W. Oscillation of certain higher-order neutral partial functional differential equations. Springer Plus. 2016;5(459):1-8.
- Lin WX. Some oscillation theorems for systems of even order quasilinear partial differential equations. Appl Math Comput. 2004;152:337-349.
- Wang PG, Yu YH, Caccetta L. Oscillation criteria for boundary value problems of high-order partial functional differential equations. J Comput Appl Math. 2007;206:567-577.
- Vladimirov VS. Equations of Mathematics Physics, Nauka, Moscow, 1981.
- Kiguradze IT. On the oscillation of solutions of the equation . Math Sb. 1964;65:172-187 (in Russian).
- Philos Ch.G. A new criterion for the oscillatory and asymptotic behavior of delay differential equations. Bull Acad Pol Sci Ser Sci Math. 1981;39:61-64.
- Hardy GH, Littlewood JE, Polya G. Inequalities. Cambridge University Press, Cambridge, UK, 1988.