Impulsive functional differential equations with variable times (original) (raw)
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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].
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].
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.
Boundary Value Problems for Impulsive Differential Equations and Avery Type Fixed Point Theorems
In this article we apply an extension of an Avery type fixed point theorem to a family of boundary value problems for a second order ordinary differential equation with impulse. The theorem employs concave and convex functionals defined on a cone in a Banach space. The definition of the cone and the definitions of the functionals are impacted by the impulse. It is shown that the impulse in the unknown function plays little to no role and the impulse in velocity of the unknown function satisfy properties completely analogous to the properties of the nonlinear forcing term.