Vol. 4 (12) pp. 1793-1796

ON STABILITY OF ZERO SOLUTION OF SOME TYPES OF FIFTH ORDER.

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  • Department of Mathematics,College of Science, University of Baghdad.
  • Department of Mathematics, College of Ibn-AL Haitham, University of Baghdad.
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Abstract

This paper is illustrates the sufficient conditions of theuniformly asymptotically stableand the bounded of the zero solution of fifth order nonlinear differential equation with a variable delay ?(t)as given by the following: x^((5) )+?(x ? ) x^((4) )+f(x(t-?(t) ),x ?(t-?(t) ),?,x^((4) ) (t-?(t) ) ) x ?(t)+ax ?(t)+g(x(t-?(t) ),x ?(t-?(t) ),?,x^((4) ) (t-?(t) ) ) x ?(t)+h(x(t-?(t) ) )+k(x ?(t-?(t) ) ) =P( t ,x(t),x(t-?(t) ),x ?(t),x ?(t-?(t) ),?,x^((4) ) (t) ?,x?^((4) ) (t-?(t) ) )?(1) Where x?R, ?(t)is variables delay, a is positive constant, ?,f,g,h,k and p are continuous functions in R,R^5,R^5,R,R, and R^+×R^10, respectively, and the dots in(1) denote differentiation respect with to t,t?R^+.

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References

  1. Burton T.A.,"Stability and Periodic Solutions of Ordinary and Functional Differential Equations", Academic Press, Orlando (1985).
  2. TuncCemil,"A Study of the Stability and Boundednessof the Solutions of Nonlinear Differential Equations of Fifth Order ", Indian J. pure appl. Math.,33(4), 519–529,2002.
  3. Buthainah A. A. Ahmed, May Mohammed Hilal, " stabilityand Instability of some Types of Delay Differential Equations", Ph.D. Dissertation, Mathematics Science, University of Mosul, 2015.
 

How to Cite This Article

Buthainah A. A and May M. Hilal. (2016); ON STABILITY OF ZERO SOLUTION OF SOME TYPES OF FIFTH ORDER., Int. J. of Adv. Res., 4 (12), 1793-1796, ISSN 2320-5407.

Corresponding Author

May M. Hilal

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