An existence result for a new class of impulsive functional differential equations with delay

Abstract We prove the existence of bounded solutions of a new class of retarded functional differential equations with non-instantaneous impulses and delay on an unbounded domain. An application example is also included.

[1]  Gang Li,et al.  Existence results for semilinear differential equations with nonlocal and impulsive conditions , 2010 .

[2]  M. Benchohra,et al.  Impulsive differential equations and inclusions , 2006 .

[3]  Hernán R. Henríquez,et al.  Existence of solutions for impulsive partial neutral functional differential equations , 2007 .

[4]  On the compactness of the evolution operator generated by certain nonlinear Ω-accretive operators in general Banach spaces , 1995 .

[5]  Donal O'Regan,et al.  On a new class of abstract impulsive differential equations , 2012 .

[6]  A compact evolution operator generated by a nonlinear time-dependentm-accretive operator in a Banach space , 1995 .

[7]  V. Staicu,et al.  Multivalued evolution equations with nonlocal initial conditions in Banach spaces , 2007 .

[8]  Mouffak Benchohra,et al.  Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions , 2009 .

[9]  E. Feng,et al.  Optimality condition of the nonlinear impulsive system in fed-batch fermentation , 2008 .

[10]  Juan J. Nieto,et al.  Impulsive periodic solutions of first‐order singular differential equations , 2008 .

[11]  Shujing Gao,et al.  Pulse Vaccination Strategy in an Epidemic Model with Two Susceptible Subclasses and Time Delay , 2011 .

[12]  Juan J. Nieto,et al.  Solvability of impulsive neutral evolution differential inclusions with state-dependent delay , 2009, Math. Comput. Model..

[13]  T. Cardinali,et al.  Impulsive mild solutions for semilinear differential inclusions with nonlocal conditions in Banach spaces , 2012 .

[14]  Alberto d'Onofrio,et al.  On pulse vaccination strategy in the SIR epidemic model with vertical transmission , 2005, Appl. Math. Lett..

[15]  Vittorio Colao,et al.  Existence of solutions for a second-order differential equation with non-instantaneous impulses and delay , 2016 .

[16]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[17]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[18]  Lamberto Cesari,et al.  Asymptotic Behavior and Stability Problems in Ordinary Differential Equations , 1963 .

[19]  Jin Liang,et al.  Existence of classical solutions to nonautonomous nonlocal parabolic problems , 2005 .

[20]  D. Bainov,et al.  Impulsive Differential Equations: Periodic Solutions and Applications , 1993 .

[21]  W. A. Coppel Dichotomies and stability theory , 1971 .

[22]  Haim Brezis,et al.  Semi-linear second-order elliptic equations in L 1 , 1973 .

[23]  Kezan Li,et al.  Nonlinear impulsive system of fed-batch culture in fermentative production and its properties , 2006 .

[24]  Existence of solutions on compact and non-compact intervals for semilinear impulsive differential inclusions with delay , 2008 .

[25]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.