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Walther, H. (2003) The Solution Manifold and C1-Smoothness for Differential Equations with State-Dependent Delay. Journal of Differential Equations, 195, 46-65.
https://doi.org/10.1016/j.jde.2003.07.001

has been cited by the following article:

• TITLE: Existence of Exponential Attractors for Suspension Bridge Equations with State Delay

  AUTHORS: Ruonan Wang, Qiaozhen Ma

  KEYWORDS: Contractive Function, Well-Posedness, Time-Dependent Global Attractors

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.11, November 5, 2025

  ABSTRACT: This paper studies the nonlocal suspension bridge equation with state-dependent delay in 2D space and the existence of attractors. First, by using Banach fixed point theorem and operator semigroup theory, the existence and uniqueness of mild solutions and continuous dependence on initial values of suspension bridge equations with state delay are proved. Then the bounded dissipativity of the related semi-group and the quasi-stability of the system are verified to obtain a global attractor with finite fractal dimension the existence of the attractor in the generalized index.