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2. A new continuous dependence result for impulsive retarded functional differential equations

Creator:
Federson, Márcia and Mesquita, Jaqueline Godoy
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, diferenciální rovnice, mathematics, differential equations, retarded functional differential equation, impulse local existenc, impulse local existence uniqueness, continuous dependence on parameters, 13, and 51
Language:
English
Description:
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., Márcia Federson, Jaqueline Godoy Mesquita., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals

Creator:
Federson, Márcia
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Monotone Convergence Theorem, Kurzweil vector integral, and ordered normed spaces
Language:
English
Description:
We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil, $\int _R{\mathrm d}\alpha (t) f(t)$, where $R$ is a compact interval of $\mathbb{R}^n$, $\alpha $ and $f$ are functions with values on $L(Z,W)$ and $Z$ respectively, and $Z$ and $W$ are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral, $\int _R\alpha (t)\mathrm{d}f(t)$, as well as to unbounded intervals $R$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public