Annali di Matematica Pura ed Applicata

, Volume 95, Issue 1, pp 293–301

# Further stability and boundedness results for the solutions of some differential equations of the fourth order

• B. S. Lalli
• W. A. Skrapek
Article

## Summary

In this paper sufficient conditions (Theorem 1 and Corollary 1) for the asymptotic stability (in the large) of the trivial solutions x=0 of the differential equations
$$D_1 \left( x \right) = x^{\left( 4 \right)} + f_1 \left( {\ddot x} \right)\dddot x + f_2 \left( {\dot x,\ddot x} \right) + g\left( {x,\dot x} \right) + h\left( {x,\dot x} \right) = 0,$$
and
$$D_2 \left( x \right) = x^{\left( 4 \right)} + F_1 \left( {\ddot x} \right)\dddot x + F_2 \left( {\dot x,\ddot x} \right)\ddot x + G\left( {x,\dot x} \right)\dot x + H\left( {x,\dot x} \right)x = 0,$$
are given. These differential equations are more general than those considered by Harrow ([1], [2]), the authors ([5], [6]), Ezeilo [4], Tejumola [7], Reissig [8], Sinha and Hoff [9], and Cartwrifht [11]. The results reduce to those given by Harrow [1] for the equation
$$x^{\left( 4 \right)} + a_1 \dddot x + a_2 \ddot x + g\left( {\dot x} \right) + h\left( x \right) = 0.$$
A result (Theorem 2) on the boundedness of the solutions of the differential equations D1(x)==p1(t) and D2(x)=p2(t) is also established.

### Keywords

Differential Equation Fourth Order Asymptotic Stability Trivial Solution Boundedness Result

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### References

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