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Annali di Matematica Pura ed Applicata

, Volume 95, Issue 1, pp 293–301 | Cite as

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Nicola Zanichelli Editore 1973

Authors and Affiliations

  • B. S. Lalli
    • 1
  • W. A. Skrapek
    • 1
  1. 1.Department of MathematicsUniversity of SaskatchewanSaskatoonCanada

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