On the stability of solutions of certain fourth order delay differential equations.(English)Zbl 1047.34089

The author considers the fourth-order nonlinear differential equations $x^{(4)} + \alpha_1 x^{(3)} + \alpha_2 \ddot x + \alpha_3 \dot x + f(x(t-r))=0,$ and $x^{(4)} + \alpha_1 x^{(3)} + \alpha_2 \ddot x + \phi( \dot x(t-r)) + f(x)=0,$ where $$r, \alpha_1,\alpha_2, \alpha_3$$ are positive constants, $$\phi(x), f(x)$$ are continuous, $$\phi(0)=f(0)=0$$. By constructing Lyapunov functionals, the author derives conditions for the asymptotic stability of the zero-solution to the equations above.

MSC:

 34K20 Stability theory of functional-differential equations

Keywords:

equations with delay; stability
Full Text:

References:

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