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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 40 Issue: 2

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

Coşkun Yakar
muhammed Çiçek
Sayfa
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Yayın Tarihi
2011-02-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We support our new results with analytic examples and numerical applications.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:These are unified with Lyapunov-like functions to establish a variational comparison result.
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Sonuç & Katkı:We support our new results with analytic examples and numerical applications.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Initial time difference · Perturbed differential systems · Boundedness and Lagrange stability

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.

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Bu Makaleye Atıf Yap

Yakar, C., Çiçek, M. (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, Volume: 40 Issue: 2. https://ajindex.com/articles/1403658

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Kaynakça (13)

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  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.
  9. 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.
  10. Yakar, C. and Shaw, M. D. Initial time difference stability in terms of two Measures and
  11. variational comparison resultDCDIS Ser. A: Mathematical Analysis. 15, 417–425, 2008.
  12. Yakar, C. and Shaw, M. D. Practical stability in terms of two measures with initial time
  13. difference, Nonlinear Analysis: Theory, Methods & Applications. 71, 781–785, 2009.