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Vietnam Journal of Mathematics 38:4 (2010) 453-466

 

On the Stability and Boundedness of Solutions in a Class of Nonlinear Differential

Equations of Fourth Order with Constant Delay

Cemil TunÁ

Abstract. In this paper, we discuss the stability and boundedness of solutions of nonlinear delay differential equation of fourth-order:

x(4)(t) + f1(x''(t))x'''(t) + f2(x''(t - r)) + g(x'(t - r)) + h(x(t - r)) = p(t,x(t),x(t-r),x'(t),x'(t-r),x''(t),x''(t-r),x'''(t)),

when p = 0 and, p ≠ 0 respectively, where r >0 is a constant delay. In proving our main results, we use the Lyapunov functional approach.

2000 Mathematics Subject Classification: 34K20.

Keywords: Nonlinear differential equation, fourth order, delay, stability, boundedness, Lyapunov functional.

 

 

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