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THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS

Year 2011, Volume: 40 Issue: 2, 305 - 330, 01.02.2011

Coşkun Yakar  muhammed Çiçek

Abstract

This paper investigates the initial time difference equi-boundedness criteria in terms of two measures, initial time difference boundedness and Lagrange Stability in terms of two measures. These are unified with Lyapunov-like functions to establish a variational comparison result. We support our new results with analytic examples and numerical applications.

Keywords

Initial time difference Perturbed differential systems Boundedness and Lagrange stability In terms of two measures Variational comparison result 2010 AMS Classification: 34 A 05

References

  • Lakshmikantham, V. and Deo, S. G. Method of Variation of Parameters for Dynamic Sys- tems(Gordon and Breach Science Pub., Amsterdam, 1998).
  • Lakshmikantham, V. and Leela, S. Differential and Integral Inequalities, Vol. 1 and Vol 2 (Academic Press, New York, 1969).
  • Lakshmikantham, V. and Liu, X. Stability Analysis in Terms of Two Measures (World Scientific, Singapore, 1992).
  • Lakshmikantham, V. Matrosov, V. M. and Sivasundaram, S. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems(Kluwer Academic Pub., London, 1991).
  • Lakshmikantham, V. and Vatsala, A. S. Differential inequalities with time difference and application, J. Ineq. Appl. 3, 233–244, 1999.
  • Liu, X. and Shaw, M. D. Boundedness in terms of two measures for perturbed systems by generalized variation of parameters, Communications in Applied Analysis 5, 435–444, 2001.
  • Shaw, M. D. and Yakar, C. Generalized variation of parameters with initial time difference and a comparison result in terms of Lyapunov-like functions, Int. J. Non-linear Diff. Eqs. Theory-Method and Applications 5, 86–108, 1999.
  • Yakar, C. Boundedness criteria with initial time difference in terms of two measures, DCDIS Ser. A: Math. Anal. 14 Advances in Dynamical Systems, suppl. S2, 270–275, 2007.
  • Yakar, C. and Shaw, M. D. A comparison result and Lyapunov stability criteria with initial time difference, DCDIS Ser. A: Mathematical Analysis 12 (6), 731–741, 2005.
  • Yakar, C. and Shaw, M. D. Initial time difference stability in terms of two Measures and
  • variational comparison resultDCDIS Ser. A: Mathematical Analysis. 15, 417–425, 2008.
  • Yakar, C. and Shaw, M. D. Practical stability in terms of two measures with initial time
  • difference, Nonlinear Analysis: Theory, Methods & Applications. 71, 781–785, 2009.

THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS

Year 2011, Volume: 40 Issue: 2, 305 - 330, 01.02.2011

Coşkun Yakar  muhammed Çiçek

Abstract

References

  • Lakshmikantham, V. and Deo, S. G. Method of Variation of Parameters for Dynamic Sys- tems(Gordon and Breach Science Pub., Amsterdam, 1998).
  • Lakshmikantham, V. and Leela, S. Differential and Integral Inequalities, Vol. 1 and Vol 2 (Academic Press, New York, 1969).
  • Lakshmikantham, V. and Liu, X. Stability Analysis in Terms of Two Measures (World Scientific, Singapore, 1992).
  • Lakshmikantham, V. Matrosov, V. M. and Sivasundaram, S. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems(Kluwer Academic Pub., London, 1991).
  • Lakshmikantham, V. and Vatsala, A. S. Differential inequalities with time difference and application, J. Ineq. Appl. 3, 233–244, 1999.
  • Liu, X. and Shaw, M. D. Boundedness in terms of two measures for perturbed systems by generalized variation of parameters, Communications in Applied Analysis 5, 435–444, 2001.
  • Shaw, M. D. and Yakar, C. Generalized variation of parameters with initial time difference and a comparison result in terms of Lyapunov-like functions, Int. J. Non-linear Diff. Eqs. Theory-Method and Applications 5, 86–108, 1999.
  • Yakar, C. Boundedness criteria with initial time difference in terms of two measures, DCDIS Ser. A: Math. Anal. 14 Advances in Dynamical Systems, suppl. S2, 270–275, 2007.
  • Yakar, C. and Shaw, M. D. A comparison result and Lyapunov stability criteria with initial time difference, DCDIS Ser. A: Mathematical Analysis 12 (6), 731–741, 2005.
  • Yakar, C. and Shaw, M. D. Initial time difference stability in terms of two Measures and
  • variational comparison resultDCDIS Ser. A: Mathematical Analysis. 15, 417–425, 2008.
  • Yakar, C. and Shaw, M. D. Practical stability in terms of two measures with initial time
  • difference, Nonlinear Analysis: Theory, Methods & Applications. 71, 781–785, 2009.
There are 13 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Coşkun Yakar This is me

 muhammed Çiçek This is me

Publication Date February 1, 2011
Published in Issue Year 2011 Volume: 40 Issue: 2

Cite

APA Yakar, C., & Çiçek, . (2011). THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS. Hacettepe Journal of Mathematics and Statistics, 40(2), 305-330.
AMA Yakar C, Çiçek . THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS. Hacettepe Journal of Mathematics and Statistics. February 2011;40(2):305-330.
Chicago Yakar, Coşkun, and  muhammed Çiçek. “THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS”. Hacettepe Journal of Mathematics and Statistics 40, no. 2 (February 2011): 305-30.
EndNote Yakar C, Çiçek  (February 1, 2011) THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS. Hacettepe Journal of Mathematics and Statistics 40 2 305–330.
IEEE C. Yakar and  . Çiçek, “THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS”, Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, pp. 305–330, 2011.
ISNAD Yakar, Coşkun - Çiçek, muhammed. “THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS”. Hacettepe Journal of Mathematics and Statistics 40/2 (February 2011), 305-330.
JAMA Yakar C, Çiçek . THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS. Hacettepe Journal of Mathematics and Statistics. 2011;40:305–330.
MLA Yakar, Coşkun and  muhammed Çiçek. “THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS”. Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, 2011, pp. 305-30.
Vancouver Yakar C, Çiçek . THEORY, METHODS AND APPLICATIONS OF INITIAL TIME DIFFERENCE BOUNDEDNESS CRITERIA AND LAGRANGE STABILITY IN TERMS OF TWO MEASURES FOR NONLINEAR SYSTEMS. Hacettepe Journal of Mathematics and Statistics. 2011;40(2):305-30.

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