Periodic Boundary Value Problem for Impulsive Evolution Equations with Noncompact Semigroup

• Weifeng Ma ^[1] ; Yongxiang Li ^[1]
  1. [1] Northwest Normal University

     Northwest Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, by applying the Sadovskii’s fixed point theorem, we obtain the existence and uniqueness result of mild solution for a class of periodic boundary value problem of impulsive evolution equations in Banach space with noncompact semigroup in the case that the nonlinearity term f and impulsive functions Ik satisfy growth conditions and the measure of noncompactness conditions. And we give a specific example to illustrate our main results.

• Referencias bibliográficas
  • 1. Amann, H.: Periodic solutions of semilinear parabolic equations, Nonlinear Analysis: A Collection of Papers in honor of Erich H, (pp. 1–29)....
  • 2. Banas, J., Goebel, K.: Measure of Nonlinear in Banach Spaces, Lecture Notes in Pure Appl. Math.,vol.60, Marcel Dekker, New York, (1980)
  • 3. Benchohra, M., Henderson, J., Ntouyas, S.: Impulsive differential equations and inclusions contemporary mathematics and its applications....
  • 4. Deiling, K.: Nonlinear functional analysis. Spring-Verlag, New York (1985)
  • 5. Guo, D.: Extremal solutions of nonlinear Fredholm integral equations in order Banach spaces. Northeastern Math. J. 7(4), 416–423 (1991)
  • 6. Heinz, H.P.: On the behaviour of measure of noncompactness with respect to differentiation and integration of rector-valued functions....
  • 7. Ji, S., Li, G.: A unified approach to nonlocal impulsive differential equations with the measure of noncompactness. Adv. Differ. Equ. 2012,...
  • 8. Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of impulsive differential equations. World Scientific, Singapore (1989)
  • 9. Li, Y.: Positive solutions of abstract semilinear evolution equations and their applications. Acta. Math. Sin. 39(5), 666–672 (1996)
  • 10. Li, Y.: Existence and uniqueness of positive periodic solutions for abstract semilinear evolution equations. J. Syst. Sci. Math. Sci....
  • 11. Li, Y.: Existence of solutions for abstract semilinear evolution equations initial value problem. Acta. Math. Sin. 48(6), 1089–1094 (2005)....
  • 12. Li, B., Gou, H.: Monotone iterative method for the periodic boundary value problems of impulsive evolution equations in Banach spaces....
  • 13. Li, Q., Li, Y.: Positive periodic solutions for abstract evolution equations with delay. Positivity 25, 379–397 (2021)
  • 14. Li, Q., Wei, M.: Existence and asymptotic stability of periodic solutions for impulsive delay evolution equations. Adv. Difference Equ....
  • 15. Liu, J.: Nonlinear impulsive evolution equations. Dyn. Contin. Discret. Impuls. Syst. 6(1), 77–85 (1999)
  • 16. Pazy, A.: Semigroups of linear operators and applications to partial differential equations. SpringerVerlag, Berlin (1983)
  • 17. Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)
  • 18. Sun, J., Zhang, X.: The fixed point theorem of convex-power condensing operator and applications to abstract semilinear evolution. Acta....
  • 19. Zhang, X.: Lower and upper solutions for delay evolution equations with nonlocal and impulsive conditions. Electron. J. Differ. Equ. 31,...