A Second-order Impulsive Cauchy Problem
نویسنده
چکیده
We study the existence of mild and classical solutions for an abstract second-order impulsive Cauchy problem modeled in the form ü(t) = Au(t)+f(t,u(t),u̇(t)), t ∈ (−T0,T1), t ≠ ti; u(0) = x0, u̇(0) = y0; u(ti) = I1 i (u(ti)), u̇(ti) = I2 i (u̇(t+ i )), where A is the infinitesimal generator of a strongly continuous cosine family of linear operators on a Banach space X and f , I1 i , I 2 i are appropriate continuous functions.
منابع مشابه
Existence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales
In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.
متن کاملAn Existence Result for Nonlocal Impulsive Second-Order Cauchy Problems with Finite Delay
and Applied Analysis 3 Then, for every t ∈ J, we have
متن کاملImpulsive Integrodifferential Equations Involving Nonlocal Initial Conditions
We focus on a Cauchy problem for impulsive integrodifferential equations involving nonlocal initial conditions, where the linear part is a generator of a solution operator on a complex Banach space. A suitable mild solution for the Cauchy problem is introduced. The existence and uniqueness of mild solutions for the Cauchy problem, under various criterions, are proved. In the last part of the pa...
متن کاملExistence Results for Nonlinear Boundary Value Problems of Impulsive Fractional Integrodifferential Equations
In this paper, we investigate the existence result for nonlinear impulsive fractional integro-differential equations with boundary conditions by using fixed point theorem and Green's function. I. INTRODUCTION The topic of fractional differential equations has received a great deal of attention from many scientists and researchers during the past decades; see [1-7]. This is mostly due to the fac...
متن کاملNUMERICAL SOLUTIONS OF SECOND ORDER BOUNDARY VALUE PROBLEM BY USING HYPERBOLIC UNIFORM B-SPLINES OF ORDER 4
In this paper, using the hyperbolic uniform spline of order 4 we develop the classes of methods for the numerical solution of second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The second derivativeis approximated by the three-point central difference scheme. The approximate results, obtained by the proposed method, confirm theconvergence o...
متن کامل