Further results on global stability of solutions of certain third-order nonlinear differential equations

Mathew Omonigho Omeike

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2008)

  • Volume: 47, Issue: 1, page 121-127
  • ISSN: 0231-9721

Abstract

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Sufficient conditions are established for the global stability of solutions of certain third-order nonlinear differential equations. Our result improves on Tunc’s [10].

How to cite

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Omeike, Mathew Omonigho. "Further results on global stability of solutions of certain third-order nonlinear differential equations." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 47.1 (2008): 121-127. <http://eudml.org/doc/32464>.

@article{Omeike2008,
abstract = {Sufficient conditions are established for the global stability of solutions of certain third-order nonlinear differential equations. Our result improves on Tunc’s [10].},
author = {Omeike, Mathew Omonigho},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {nonlinear differential equation; trivial solution; global stability; Lyapunov’s method; global stability; nonlinear differential equations; third order},
language = {eng},
number = {1},
pages = {121-127},
publisher = {Palacký University Olomouc},
title = {Further results on global stability of solutions of certain third-order nonlinear differential equations},
url = {http://eudml.org/doc/32464},
volume = {47},
year = {2008},
}

TY - JOUR
AU - Omeike, Mathew Omonigho
TI - Further results on global stability of solutions of certain third-order nonlinear differential equations
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2008
PB - Palacký University Olomouc
VL - 47
IS - 1
SP - 121
EP - 127
AB - Sufficient conditions are established for the global stability of solutions of certain third-order nonlinear differential equations. Our result improves on Tunc’s [10].
LA - eng
KW - nonlinear differential equation; trivial solution; global stability; Lyapunov’s method; global stability; nonlinear differential equations; third order
UR - http://eudml.org/doc/32464
ER -

References

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  1. Barbashin E. A.: Lyapunov Functions., Nauka, Moscow, , 1970. (1970) 
  2. Ezeilo J. O. C., On the stability of solutions of certain differential equations of the third order, Quart. J. Math. Oxford Ser. 11 (1960), 64–69. (1960) Zbl0090.06603MR0117394
  3. Goldwyn M., Narendra S.: Stability of Certain Nonlinear Differential Equation Using the Second Method of Lyapunov., Craft Lab. Harvard Univ., Cambridge, MA, , 1963, pp. 1–14. (1963) 
  4. Kraovkii N. N.: Stability of Motion., Stanford University Press, Stanford, CA, , 1963. (1963) 
  5. Ogurtsov A. I., On the stability of the solutions of some nonlinear differential equations of the third and forth order, Ivz. Vyssh. Uchebn. Zaved. Mat. 10 (1959), 200–209. (1959) 
  6. Qin Y., Wan M., Wang L.: Theory, Applications of Stability of Motions., Academic Press, Beijing, , 1981. (1981) MR0701397
  7. Qian C., On global stability of third-order nonlinear differential equations, Nonlinear Analysis 42 (2000), 651–661. Zbl0969.34048MR1776296
  8. Qian C., Asymptotic behavior of a third-order nonlinear differential equation, J. Math. Anal. Appl. 284 (2003), 191–205. Zbl1054.34078MR1996127
  9. Omeike M. O., Further results on global stability of third-order nonlinear differential equations, Nonlinear Analysis 67 (2007) 3394–3400. Zbl1129.34323MR2350895
  10. Tunc C., Global stability of solutions of certain third-order nonlinear differential equations, Panamer. Math. J. 14, 4 (2004), 31–35. Zbl1065.34047MR2102487
  11. Tunc C., On the asymptotic behavior of solutions of certain third-order nonlinear differential equations, J. Appl. Math. Stoch. Anal. 1 (2005), 29–35. Zbl1077.34052MR2140325
  12. Reissig, R, Sansone G., Conti R.: Nonlinear Differential Equations of Higher Order., Noordhoff Inter. Pub., Leyden, , 1974. (1974) MR0344556
  13. Shimanov S. N., On the stability of the solution of a nonlinear equation of the third order, Prikl. Mat. Mekh. 17 (1953), 369–372. (1953) MR0055523
  14. Wang L., Wang M., Analysis of construction of Lyapunov functions of third-order nonlinear systems, Acta Math. Appl. Sin. 6 (1983), 309–323. (1983) MR0748533

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