Método da média para equações diferenciais funcionais retardadas impulsivas via equações diferenciais generalizadas / Averaging method for retarded functional differential equations with impulses by generalized ordinary differential equations

AUTOR(ES)
DATA DE PUBLICAÇÃO

2009

RESUMO

In this present work, we condider the following initial value problem for a retarded functional differential equation with impulses { x POINT= varepsilonf (t, x IND.t), t DIFFERENTt IND. k, DELTAx(t IND. k) = varepsilonI IND. k(x ( t IND.k)), k = 0, 1, 2, ... x IND. t IND.0= phi, where f está defined in a open set OMEGAde R x G POT. -([- r, 0], R POT. n), r >0, and takes values in R POT. n, varepsilonG POT. - ([ - r, 0], R POT.n), r .0, where G POT -([ - r, 0], R POT. n) denotes the space of regulated functions from [ - r, 0] to R POT. nwhich are left continuous. Furthermore, t IND.0 k) - x (t IND. k). The impulse operators I IND. k, k = 0, 1, ... are continuous mappings from R POT. nto R POT. n. For each x varepsilonG POT. -([- r, THE INFINITE), R POT. n), t ARROWf (t, x IND. t) is locally Lebesgue integrable and its indefinite integral satisfies a Carathéodory. Moreover, f é Lipschitzian with respect to the second variable. We define f IND. 0( phi) = lim ON T ARROWTHE INFINITE1 SUP. T INT. SUP. T INF. T IND.0f (t, PSI) dt and I IND. 0(x) = lim ON T ARROWTHE INFINITE1 SUP. TSIGMAIND. 0 0(y (t))], y IND. t IND. 0 = phi. Then we prove that, under certain conditions, the solution x(t) of (1) in aproximates the solution y(t) de (2) in an asymptotically large time interval

ASSUNTO(S)

método da média equações diferenciais impulsivas equações diferenciais funcionais retardadas impulsive differential equations equações diferenciais generalizadas retardedf functional differential equations averaging generalized ordinary differential equations

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