Research Article

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

Volume: 40 Number: 2 February 1, 2011
  • Coşkun Yakar
  •  muhammed Çiçek
EN TR

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

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

References

  1. Lakshmikantham, V. and Deo, S. G. Method of Variation of Parameters for Dynamic Sys- tems(Gordon and Breach Science Pub., Amsterdam, 1998).
  2. Lakshmikantham, V. and Leela, S. Differential and Integral Inequalities, Vol. 1 and Vol 2 (Academic Press, New York, 1969).
  3. Lakshmikantham, V. and Liu, X. Stability Analysis in Terms of Two Measures (World Scientific, Singapore, 1992).
  4. Lakshmikantham, V. Matrosov, V. M. and Sivasundaram, S. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems(Kluwer Academic Pub., London, 1991).
  5. Lakshmikantham, V. and Vatsala, A. S. Differential inequalities with time difference and application, J. Ineq. Appl. 3, 233–244, 1999.
  6. 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.
  7. 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.
  8. 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.

Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

Coşkun Yakar This is me

 muhammed Çiçek This is me

Publication Date

February 1, 2011

Submission Date

May 12, 2014

Acceptance Date

-

Published in Issue

Year 2011 Volume: 40 Number: 2

APA
Yakar, C., & Çiçek, muhammed. (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. https://izlik.org/JA86AG32XR
AMA
1.Yakar C, 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. 2011;40(2):305-330. https://izlik.org/JA86AG32XR
Chicago
Yakar, Coşkun, and  muhammed 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): 305-30. https://izlik.org/JA86AG32XR.
EndNote
Yakar C, Çiçek muhammed (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
[1]C. Yakar and  muhammedÇiçek, “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, Feb. 2011, [Online]. Available: https://izlik.org/JA86AG32XR
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 1, 2011): 305-330. https://izlik.org/JA86AG32XR.
JAMA
1.Yakar C, 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. 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, Feb. 2011, pp. 305-30, https://izlik.org/JA86AG32XR.
Vancouver
1.Coşkun Yakar,  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 [Internet]. 2011 Feb. 1;40(2):305-30. Available from: https://izlik.org/JA86AG32XR