A new continuous dependence result for impulsive retarded functional differential equations

Czechoslovak Mathematical Journal

Jaqueline Godoy Mesquita¹  Márcia Federson² 

[1] Departamento de Matemática, Universidade de Brasília, Campus Universitário Darcy Ribeiro, Asa Norte 70910-900, Brasília-DF, Brazil;Instituto de Cincias Matemáticas ede Computao, Universidade de So Paulo, Campus de So Carlos, Avenida Trabalhador So Carlense, 400, Caixa Postal 668, 13560-970 So Carlos-SP, Brazil

关键词: retarded functional differential equation;    impulse local existence;    impulse local existence uniqueness;    continuous dependence on parameters;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume that the limiting equation is an impulsive RFDE whose initial condition is the uniform limit of the sequence of the initial data and whose solution exists and is unique. Then, for sufficient large indexes, the elements of the sequence of impulsive retarded initial value problem admit a unique solution and such a sequence of solutions converges to the solution of the limiting Cauchy problem.

【 授权许可】

Unknown