Global solutions for abstract neutral differential equations (Q844954)

The author studies existence and uniqueness of a bounded solution on \(\mathbb{R}\) for some neutral systems with infinite delay. The phase space is axiomatically defined. The linear part is assumed to generate a hyperbolic semigroup on a Banach space. The nonlinear parts are assumed to be continuous and Lipschitzian with respect to the second argument. Enough conditions are provided to use the strict contraction principle to show the main results of this papers. Some example are given for a neutral partial functional differential equation with diffusion.