A new continuous dependence result for impulsive retarded functional differential equations

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: CZECHOSLOVAK MATHEMATICAL JOURNAL; v. 66, n. 1, p. 1-12, MAR 2016.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 08/02879-1 - Equações diferenciais funcionais com retardos e impulsos
• Beneficiário: Márcia Cristina Anderson Braz Federson
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 07/02731-1 - Método da média para equações diferenciais impulsivas via equações diferenciais generalizadas e aplicações
• Beneficiário: Jaqueline Godoy Mesquita
• Modalidade de apoio: Bolsas no Brasil - Mestrado