Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations
نویسندگان
چکیده
Impulsive differential equations, which arise in biology, physics, population dynamics, economics, and so forth, are a basic tool to study evolution processes that are subjected to abrupt in their states see 1–4 . Many literatures have been published about existence of solutions for first-order and second-order impulsive ordinary differential equations with boundary conditions 5–19 , which are important for complementing the theory of impulsive equations. In recent years, the solvability of the antiperiodic boundary value problems of first-order and second-order differential equations were studied by many authors, for example, we refer to 20–32 and the references therein. It should be noted that antiperiodic boundary value problems appear in physics in a variety of situations 33, 34 . Recently, the existence results were extended to antiperiodic boundary value problems for first-order impulsive differential equations 35, 36 . Very recently, Wang and Shen 37 investigated the antiperiodic boundary value problem for a class of second-order differential equations by using Schauder’s fixed point theorem and the lower and upper solutions method. Inspired by 35–37 , in this paper, we investigate the antiperiodic boundary value problem for second-order impulsive nonlinear differential equations of the form
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