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On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument

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Abstract

This paper investigates stability and boundedness of solutions to third order nonlinear differential equation with retarded argument:

$$\begin{array}{l}x'''(t)+\varphi\bigl(x(t-r),x'(t-r),x''(t-r)\bigr)x''(t)\\\qquad{}+\psi\bigl(x'(t-r)\bigr)+h\bigl(x(t-r)\bigr)\\\quad=p\bigl(t,x(t),x(t-r),x'(t),x'(t-r),x''(t)\bigr).\end{array}$$

By the use of the Lyapunov functional, sufficient conditions for stability and boundedness of solutions to the considered equations are obtained. Examples are introduced throughout the paper for illustrations.

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  1. Department of Mathematics, Faculty of Arts and Sciences, Yüzüncü Yıl University, 65080, Van, Turkey

    Cemil Tunç

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  1. Cemil Tunç
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Tunç, C. On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument. Nonlinear Dyn 57, 97–106 (2009). https://doi.org/10.1007/s11071-008-9423-6

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