Geodesic
A new continuous dependence result for impulsive retarded functional differential equations
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 1-12
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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.
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.
DOI : 10.1007/s10587-016-0233-6
Classification : 34K05, 34K45
Keywords: retarded functional differential equation; impulse local existence; impulse local existence uniqueness; continuous dependence on parameters 
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Federson, Márcia; Mesquita, Jaqueline Godoy. A new continuous dependence result for impulsive retarded functional differential equations. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 1-12. doi: 10.1007/s10587-016-0233-6

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