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Stability in functional difference equations using fixed point theory

Youssef Raffoul
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회논문집 (Communications of the KMS)|제29권 제1호|pp. 195-204

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참고문헌

키워드

fixed pointcontraction mappingcompletely delayeddiscreteLyapunov functionals
주제분류수학

초록

We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t − r)).

Abstract

We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t − r)).

참고문헌 (15)

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  3. W. Kelley, "Difference Equations" (2001), Academic Press
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  5. Mariette R. Maroun, "PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY", 대한수학회지, 42(2), pp.65~78 (2005), 대한수학회
  6. J. Migda, "Asymptotic behavior of solutions of nonlinear difference equations", Math. Bohem, 129(4), pp.349~359 (2004)
  7. M. Islam, "Boundedness and Stability For Nonlinear Delay Difference Equations Employing Fixed Point Theory", in review, ~
  8. Y. Raffoul, "General theorems for stability and boundedness for nonlinear functional discrete systems", J. Math. Anal. Appl, 279(2), pp.639~650 (2003)
  9. Y. Raffoul, "Periodicity in general delay non-linear difference equations using fixed point theory", J. Difference Equ. Appl, 10(13-15), pp.1229~1242 (2004)
  10. Y. Raffoul, "Stability and periodicity in discrete delayed equations", J. Math. Anal. Appl, 324(2), pp.1356~1362 (2006)
  11. Y. Raffoul, "Inequalities That Lead To Exponential Stability And Instability In Delay Difference Equations", J. Inequal. Pure Appl. Math, 10(3), pp.9~ (2009)
  12. C. Qian, "On global attractivity of nonlinear delay difference equations with a forcing term", J. Difference Equ. Appl, 11(3), pp.227~243 (2005)
  13. D. C. Zhang, "Global behavior of solutions of a nonlinear difference equation", Appl. Math. Comput, 159(1), pp.29~35 (2004)
  14. G. Zhang, "Periodicity and attractivity of a nonlinear higher order difference equation", Appl. Math. Comput, 161(2), pp.395~401 (2005)
  15. H. Zhu, "Asymptotic behavior of solutions for a class of delay difference equation", Ann. Differential Equations, 21(1), pp.99~105 (2005)

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