Convergence of the solutions for the equation x ( i v ) + a x ⃛ + b x ¨ + g ( x ˙ ) + h ( x ) = p ( t, x, x ˙, x ¨, x ⃛ )

Anthony Uyi Afuwape

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-7

Abstract:

This paper is concerned with differential equations of the form x ( i v ) + a x ⃛ + b x ¨ + g ( x ˙ ) + h ( x ) = p ( t , x , x ˙ , x ¨ , x ⃛ ) where a , b are positive constants and the functions g , h and p are continuous in their respective arguments, with the function h not necessarily differentiable. By introducing a Lyapunov function, as well as restricting the incrementary ratio η − 1 { h ( ζ + η ) − h ( ζ ) } , ( η ≠ 0 ) , of h to a closed sub-interval of the Routh-Hurwitz interval, we prove the convergence of solutions for this equation. This generalizes earlier results.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:326851

DOI: 10.1155/S0161171288000882

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