Monotone iterative method for abstract impulsive integro-differential equations with nonlocal conditions in Banach spaces.

Autor: Chen, Pengyu
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Jazyk: angličtina
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Druh dokumentu: Non-fiction
ISSN: 0862-7940
Abstrakt: Abstract: In this paper we use a monotone iterative technique in the presence of the lower and upper solutions to discuss the existence of mild solutions for a class of semilinear impulsive integro-differential evolution equations of Volterra type with nonlocal conditions in a Banach space $E$ \cases u'(t)+Au(t)= f(t,u(t),Gu(t)),\quad t\in J, t\neq t_k, \Delta u |_{t=t_k}=u(t_k^+)-u(t_k^-)=I_k(u(t_k)),\quad k=1,2,\dots,m, u(0)=g(u)+x_0, where $A D(A)\subset E\to E$ is a closed linear operator and $-A$ generates a strongly continuous semigroup $T(t)$ $(t\geq0)$ on $E$, $f\in C(J\times E\times E, E)$, $J=[0,a]$, $0
Databáze: Katalog Knihovny AV ČR