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Title of Journal: J Dyn Diff Equat

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Abbravation: Journal of Dynamics and Differential Equations

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Springer US

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DOI

10.1016/0040-6090(78)90339-5

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ISSN

1572-9222

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Second Order Abstract Neutral Functional Different

Authors: Hernán R Henríquez Claudio Cuevas
Publish Date: 2015/09/08
Volume: 29, Issue: 2, Pages: 615-653
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Abstract

In this paper we are concerned with a class of second order abstract neutral functional differential equations with finite delay in a Banach space We establish the existence of mild and classical solutions for the nonlinear equation and we show that the map defined by the mild solutions of the linear equation is a strongly continuous semigroup of bounded linear operators on an appropriate space We use this semigroup to establish a variation of constants formula to solve the inhomogeneous linear equationThe authors are very grateful to the anonymous reviewer for their dedicated work which has allowed us to significantly improve the original manuscript The first author was supported partially by CONICYT under Grant FONDECYT 1130144 and DICYTUSACH and the second author was supported partially by CNPq/Brazil under Grant 478053/20134

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Other Papers In This Journal:
  1. Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay
  2. A Grobman–Hartman Theorem for Control Systems
  3. Invariant Tori of Full Dimension for Second KdV Equations with the External Parameters
  4. Complete Global and Bifurcation Analysis of a Stoichiometric Predator–Prey Model
  5. Existence of Rotating Spots with Spatially Dependent Feedback in the Plane in a Wave Front Interaction Model
  6. A Permutation Related to Non-compact Global Attractors for Slowly Non-dissipative Systems
  7. Random Attractor Associated with the Quasi-Geostrophic Equation
  8. Existence and Asymptotic Behavior of Solutions to Semilinear Wave Equations with Nonlinear Damping and Dynamical Boundary Condition
  9. A Free Boundary Problem for the Predator–Prey Model with Double Free Boundaries
  10. Stability of Solitary Waves for the Generalized Higher-Order Boussinesq Equation
  11. A Few Remarks on Partially Hyperbolic Diffeomorphisms of $${\mathbb T}^3$$ Isotopic to Anosov
  12. On The Number of Characteristic Lines for Homogeneous Vector Fields
  13. Eigenvalues of Self-Similar Solutions of the Dafermos Regularization of a System of Conservation Laws via Geometric Singular Perturbation Theory
  14. Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations
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