Advertisement

On the boundedness and stability properties of solutions of some differential equations of the fifth order

  • 29 Accesses

  • 4 Citations

Summary

The paper investigates the equation (1.1) in two cases:(i) p ≡ 0,(ii) p(≠ 0) is bounded. For the case(i) the asymptotic stability (in the large) of the trivial solution x=0 is established, and for the case(ii) a boundedness result is deduced with a bound dependent on the initial conditions. These results on (1.1) are comparable in generality to known results of third and fourth order systems.

References

  1. [1]

    E. A. Barbasin,On the stability of the solution of a certain non-linear equation of the third order, Priklad. Mat. Meh.,16 (1952), pp. 629–632 (in Russian, translation available from D.S.I.R.).

  2. [2]

    M. L. Cartwright,On the stability of solutions of certain differential equations of the fourth order, Quart. J. Mech. and Appl. Math.,9 (1956), pp. 185–194.

  3. [3]

    J. O. C. Ezeilo,A stability result for solutions of a certain fourth order differential equation, J. London Math. Soc.,37 (1962), pp. 28–32.

  4. [4]

    J. O. C. Ezeilo,On the boundedness and the stability of solutions of some differential equations of the fourth order, J. Math. Anal. and Appl.,5 (1962), pp. 136–146.

  5. [5]

    J. O. C. Ezeilo,Stability results for the solutions of some third and fourth order differential equation, Ann. Mat. pura e appl.,4 (1964), pp. 233–250.

  6. [6]

    M. Harrow,On the stability of solutions of some non homogeneous differential equations of the fourth order, SIAM J. Math. Anal.,1 (1970), pp. 98–103.

  7. [7]

    S. W. McCuskey,An Introduction to Advanced Dynamics, Addison Wesley Publishing Co., Inc., Reading, Mass., U.S.A., 1959.

  8. [8]

    A. I. Ogurtsov,The stability of solutions of two non-linear differential equations of the third and fourth orders, PMM Appl. Math. Mech.,23 (1959), p. 247.

  9. [9]

    E. N. Rosenvasser,On the stability of non-linear control systems described by fifth and sixth order differential equations, Automat. Remote Control,19, no. 2 (1959), pp. 91–93.

  10. [10a]

    G. F. Sansone,Non-linear differential systems of the third and fourth order, Proc. Conf. Prague, 1962, pp. 143–165; Publ. House Czechoslavakia Acad. Sci., Prague Academic Press, N.Y., 1963.

  11. [10b]

    R. Reissig -G. Sansone -R. Conti,Nichlineare Differentialgleichcengen, Ed. Gem, Roma, 1969.

  12. [11]

    S. N. Simanov,On the stability of a non-linear equation of the third order, Priklad. Mat. Mech.,17 (1953), p. 369 (in Russian).

Download references

Author information

Additional information

Entrata in Redazione il 27 marzo 1974.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chukwu, E.N. On the boundedness and stability properties of solutions of some differential equations of the fifth order. Annali di Matematica 106, 245–258 (1975) doi:10.1007/BF02415032

Download citation

Keywords

  • Differential Equation
  • Fourth Order
  • Asymptotic Stability
  • Stability Property
  • Trivial Solution