Boundary Value Problems for Impulsive Functional Differential Equations with Infinite Delay (original) (raw)
Australian Journal of Mathematical Analysis and Applications, 2007
In this paper, we discuss local and global existence and uniqueness results for first-order impulsive functional differential equations with multiple delay. We shall rely on a fixed point theorem of Schaefer and a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent nonlinear alternative of Leray-Schauder type in Fréchet spaces, due to Frigon and Granas [M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998) 161-168].
Journal of Mathematical Analysis and Applications, 2006
In this paper, we discuss local and global existence and uniqueness results for first-order impulsive functional differential equations with multiple delay. We shall rely on a fixed point theorem of Schaefer and a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent nonlinear alternative of Leray-Schauder type in Fréchet spaces, due to Frigon and Granas [M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998) 161-168].
Differential Equations & Applications, 2009
In this paper, we study existence of mild solutions for a second order impulsive neutral functional differential equations with state-dependent delay. By using a fixed point theorem for condensing maps combined with theories of a strongly continuous cosine family of bounded linear operators, we prove the main existence theorems. As applications of these obtained results, some practical consequences are derived for the sub-linear growth cases. And an example is also given to illustrate our main results.
On Functionally Equivalent Impulsive Delay Differential Equations
Abstract By means of certain functional relations, the equivalence of impulsive delay differential equations and impulsive differential equations is established. Based on some well known results for impulsive differential equations and for delay differential equations, nontrivial consequences on existence and nonexistence of periodic solutions of impulsive delay differential equations are obtained. Key words: Impulse, Delay, Periodic solutions, Functional equivalence.
Stability results for impulsive functional differential equations with infinite delays
Journal of Computational and Applied Mathematics, 2001
This paper studies the stability problems for a class of impulsive functional di erential equations with inÿnite delays of the form x (t) = F(t; x(•)); t¿t * ; x(t k) = J k (x(t − k)); k = 1; 2; : : : : By using the Liapunov functions and Razumikhin technique, some new Razumikhin-type theorems on stability are obtained.
Survey of Impulsive Differential Equations with Continuous Delay
In this study, we investigate first order impulsive differential equations with continuous time dependent delays and revisit some of the fundamentalconcepts in literature. Consequently, we analyse the change in the formulation of impulsive differential equation problems from studying piecewise continuously differentiable trajectories to working with piecewise absolute continuous trajectoriesand determine a suitable solution space for them.