A new continuous dependence result for impulsive retarded functional differential equations

Author(s)

Federson, Marcia ^[1] ; Mesquita, Jaqueline Godoy ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Campus Sao Carlos, Ave Trabalhador Sao Carlense, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Brasilia, Dept Matemat, Campus Univ Darcy Ribeiro, BR-70910900 Brasilia, DF - Brazil

• Document type: Journal article
• Source: CZECHOSLOVAK MATHEMATICAL JOURNAL; v. 66, n. 1, p. 1-12, MAR 2016.
• Web of Science Citations: 0

Abstract

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. (AU)

• FAPESP's process: 08/02879-1 - Equacoes diferenciais funcionais com retardos e impulsos.
• Grantee: Márcia Cristina Anderson Braz Federson
• Support Opportunities: Regular Research Grants
• FAPESP's process: 07/02731-1 - Metodo da media para equacoes diferenciais impulsivas via equacoes diferenciais generalizadas e aplicacoes.
• Grantee: Jaqueline Godoy Mesquita
• Support Opportunities: Scholarships in Brazil - Master