Well‐posedness for fully nonlinear functional differential equations

Naoki Tanaka

Mathematische Nachrichten, 2021, vol. 294, issue 8, 1595-1628

Abstract: This paper deals with the well‐posedness for the fully nonlinear functional differential equation u′(t)∈A(t)ut in a general Banach space X, where {A(t);t∈[a,b)} is a family of operators whose domains are subsets of the so‐called initial‐history space X and whose ranges are subsets of the space X. The special case where A(t)ϕ=B(t)ϕ(0)+G(t,ϕ) for t∈[a,b) and ϕ∈X with ϕ(0)∈D(B(t)) has been extensively studied so far, but there has not been a satisfactory solution to the flow invariance problem. This paper establishes the well‐posedness for the fully nonlinear functional differential equations and solves the above‐mentioned problem on flow invariance.

Date: 2021
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https://doi.org/10.1002/mana.201800498

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