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A REFINEMENT OF LYAPUNOV-TYPE INEQUALITY FOR A CLASS OF NONLINEAR SYSTEMS

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한국수학교육학회|2011.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제18권 제4호|pp. 329-336

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참고문헌

키워드

Lyapunov-type inequalitynonlinear di®erential system.
주제분류수학

초록

Some new Lyapunov-type inequalities for a class of nonlinear di®eren-tial systems, which are natural re¯nements and generalizations of the well-known Lyapunov inequality for linear second order di®erential equations, are given. The results of this paper cover some previous results on this topic.

Abstract

Some new Lyapunov-type inequalities for a class of nonlinear di®eren-tial systems, which are natural re¯nements and generalizations of the well-known Lyapunov inequality for linear second order di®erential equations, are given. The results of this paper cover some previous results on this topic.

참고문헌 (14)

  1. A.M. Lyapunov, "Sur une serie relative a la theorie des equations differentielles lineaires avec coeficient periodiques", C. R. Math. Acad. Sci., Paris, 123, pp.1248~1252 (1896)
  2. S.S. Cheng, "Lyapunov inequalities for differential and difference equations", Fasc. Math, 23, pp.25~41 (1991)
  3. S.B. Eliason, "A Lyapunov type inequality for certain nonlinear differential equation", J. London Math. Soc, 3, pp.461~466 (1970)
  4. G. Guseinov, "Lyapunov inequalities for discrete linear Hamiltonian system", Comp. Math. Appl, 45, pp.1399~1416 (2003)
  5. P. Hartman, "Ordinary Differential Equations, second ed" (1982), Birkhauser
  6. C. Lee, "Lyapunov and Wirtinger inequalities", Appl. Math. Lett, 17, pp.847~853 (2004)
  7. W. Leighton, "On Lyapunov's inequality", Proc. Amer. Math. Soc, 통권 : 33, pp.627~628 (1972)
  8. Z. Nehari, "On an inequality of Lyapunov, In "Studies in Mathematical Analysis and Related Topics"", pp.256~261 (1962), Stanford Univ. Press
  9. B.G. Pachpatte, "On Lyapunov-type inequalities for certain higher order differential equations", J. Math. Anal. Appl, 195, pp.527~536 (1995)
  10. A. Tiryaki, "Lyapunov-type inequalities for nonlinear systems", J. Math. Anal. Appl, 332, pp.497~511 (2007)
  11. X. Wang, "Lyapunov type inequalities for second order half-linear differential equations"
  12. X. Yang, "On inequalities of Lyapunov type", Appl.Math. Computation, 134, pp.293~300 (2003)
  13. X. Yang, "Lyapunov-type inequality for a class of even-order differential equa- tions", Appl. Math. Computation, 245, pp.3884~3890 (2010)
  14. X. Yang, "Lyapunov-type inequality for a class of odd-order differential equations", J. Comput. Appl. Math, 234, pp.2962~2969 (2010)

관련 논문AI추천

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