Abstract
We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the nonlinear semigroup.
Highlights
Most of the existing results about functional differential equations with finite delay have been recently under verification in the case of infinite delay
Our objective in this paper is to study the solution semigroup generated by the following partial functional differential equation with infinite delay: d dt x(t)
For every t ≥ 0, the function xt ∈ Ꮾ is defined by xt(θ) = x(t + θ), for θ ∈
Summary
Most of the existing results about functional differential equations with finite delay have been recently under verification in the case of infinite delay. Our objective in this paper is to study the solution semigroup generated by the following partial functional differential equation with infinite delay:. Where AT is a nondensely defined linear operator on a Banach space (E, | · |). The phase space Ꮾ can be the space Cγ, γ being a positive real constant, of all continuous functions φ : (−∞, 0] → E such that limθ→−∞ eγθφ(θ) exists in E, endowed with the norm φ γ := supθ≤0 eγθ|φ(θ)|, φ ∈ Cγ. For every t ≥ 0, the function xt ∈ Ꮾ is defined by xt(θ) = x(t + θ), for θ ∈
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call