The Cauchy Problem In Scale Of Banach Spaces With Deviating Variables

FIXED POINT THEORY（2021）

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摘要

In this paper, we first prove the existence and uniqueness results for the Cauchy problems in a scale of Banach spaces with deviating variables of the form u '(t) = F[t,A(t, u(t)), B(u(h(t)))]. We then apply it to study a Cauchy problem for PDEs in a Gevrey class with deviation at the derivatives. This extends some known results.

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关键词

Scale of Banach spaces, Cauchy problem, deviating variable, Gevrey function, fixed point

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