Fixed points and stability in neutral nonlinear differential equations with variable delays

• Autorzy: Ardjouni A. , Djoudi A.
• Języki publikacji: EN

Abstrakty

EN

By means of Krasnoselskii's fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307-3315], and also those of T.A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499-519] and B. Zhang [Nonlinear Anal. 63 (2005), e233-e242]. In the end we provide an example to illustrate our claim.

Słowa kluczowe

EN

fixed points; stability; nonlinear neutral differential equation; integral equation; variable delays

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 1
• Strony: 5--19
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Ardjouni A.

autor

Djoudi A.

• University of Annaba Department of Mathematics P.O. Box 12, Annaba 23000, Algeria,

Bibliografia

• [1] T.A. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover Publications, New York, 2006.
• [2] T.A. Burton, Liapunov functionals, fixed points, and stability by Krasnoselskii’s theorem, Nonlinear Stud. 9 (2001), 181–190.
• [3] T.A. Burton, Stability by fixed point theory or Liapunov’s theory: A comparison, Fixed Point Theory 4 (2003), 15–32.
• [4] T.A. Burton, Fixed points and stability of a nonconvolution equation, Proc. Amer. Math. Soc. 132 (2004), 3679–3687.
• [5] T.A. Burton, T. Furumochi, A note on stability by Schauder’s theorem, Funkcial. Ekvac. 44 (2001), 73–82.
• [6] T.A. Burton, T. Furumochi, Fixed points and problems in stability theory, Dynam. Systems Appl. 10 (2001), 89–116.
• [7] T.A. Burton, T. Furumochi, Asymptotic behavior of solutions of functional differential equations by fixed point theorems, Dynam. Systems Appl. 11 (2002), 499–519.
• [8] T.A. Burton, T. Furumochi, Krasnoselskii’s fixed point theorem and stability, Nonlinear Anal. 49 (2002), 445–454.
• [9] C.H. Jin, J.W. Luo, Stability in functional differential equations established using fixed point theory, Nonlinear Anal. 68 (2008), 3307–3315.
• [10] Y.N. Raffoul, Stability in neutral nonlinear differential equations with functional delays using fixed-point theory, Math. Comput. Modelling 40 (2004), 691–700.
• [11] D.R. Smart, Fixed Point Theorems, Cambridge Tracts in Mathematics, No. 66. Cambridge University Press, London-New York, 1974.
• [12] B. Zhang, Fixed points and stability in differential equations with variable delays, Nonlinear Anal. 63 (2005), e233–e242.