We introduce a linearization property for parameter dependent operators from a space of continuous functions into itself. This notion leads to a new implicit function theorem. As an application, we study the stability of the solutions of the integro-differential equation x′(t)=f(λ,t,x(t))+∫t0g(t,s,x(s))ds,x(0)=0, with respect to the parameter λ.
t-Osculating Operators in a Space of Continuous Functions
TROMBETTA, ALESSANDRO
2001-01-01
Abstract
We introduce a linearization property for parameter dependent operators from a space of continuous functions into itself. This notion leads to a new implicit function theorem. As an application, we study the stability of the solutions of the integro-differential equation x′(t)=f(λ,t,x(t))+∫t0g(t,s,x(s))ds,x(0)=0, with respect to the parameter λ.File in questo prodotto:
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