Existence results for mild solutions of impulsive periodic systems

• Autorzy: Yang Y. , Wang J.
• Języki publikacji: EN

Abstrakty

EN

By applying the Horn's fixed point theorem, we prove the existence of T0-periodic PC-mild solution of impulsive periodic systems when PC-mild solutions are ultimate bounded.

Słowa kluczowe

EN

impulsive periodic systems; T0-periodic PC-mild solution; Horn’s fixed point theorem; existence

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 3
• Strony: 601--616
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Yang Y.

autor

Wang J.

• Guizhou University, College of Technology, Guiyang, Guizhou 550004, P.R. China,

Bibliografia

• [1] H. Amann, Periodic solutions of semilinear parabolic equations, Nonlinear Anal.: A collection of papers in Honour of Erich Rothe, Academic Press, New York, 1978, 1–29.
• [2] N.U. Ahmed, Semigroup Theory with Applications to System and Control, Longman Scientific Technical, New York, 1991.
• [3] N.U. Ahmed, Some remarks on the dynamics of impulsive systems in Banach space, Mathematical Anal. 8 (2001), 261–274.
• [4] N.U Ahmed, K.L. Teo, S.H. Hou, Nonlinear impulsive systems on infinite dimensional spaces, Nonlinear Anal. 54 (2003), 907–925.
• [5] D.D. Bainov, P.S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical Group. Limited, New York, 1993.
• [6] X. Liu, Impulsive stabilization and applications to population growth models, Rocky Mountain J. Math. 25 (1995), 381–395.
• [7] Y. Li, F. Cong, Z. Lin, W. Liu, Periodic solutions for evolution equations, Nonlinear Anal. 36 (1999), 275–293.
• [8] J. Liu, Bounded and periodic solutions of differential equations in Banach space, J. Appl.Math. Comput. 65 (1994), 141–150.
• [9] J. Liu, Bounded and periodic solutions of differential equations in Banach space, J. Appl.Math. Comput. 65 (1994), 141–150.
• [10] J. Liu, Bounded and periodic solutions of semilinear evolution equations, Dynam. Systems Appl. 4 (1995), 341–350.
• [11] J. Liu, Bounded and Periodic Solutions of Finite Delay Evolution Equations, Nonlinear Anal. 34 (1998), 101–111.
• [12] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore-London, 1989.
• [13] J. Massera, The existence of periodic solutions of differential equations, Duke Math. J.17 (1950), 457–475.
• [14] JinRong Wang, X. Xiang, W. Wei, Linear impulsive periodic system with time-varying generating operators on Banach space, Adv. in Difference Equ., Vol. 2007, Article ID 26196, 16 pp., 2007.
• [15] JinRongWang, X. Xiang, W.Wei, Existence and global asymptotical stability of periodic solution for the T-periodic logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces, Discrete Dyn. Nat. Soc., vol.2008, Article ID 524945, 16 pp., 2008.
• [16] T. Yang, Impulsive Control Theory, Springer-Verlag, Berlin, Heidelberg, 2001.