Neutral Equations with Causal Operators

Mehran Mahdavi

Chapter 25 in Integral Methods in Science and Engineering, 2002, pp 161-166 from Springer

Abstract: Abstract This chapter deals with existence results in various function spaces, for neutral functional differential equations of the form 25.1 $$ \frac{d}{{dt}}\left[ {x(t) + \left( {Vx} \right)(t)} \right] = \left( {Wx} \right)(t),t \in \left[ {0,T} \right], $$ where, roughly speaking, V stands for a causal operator that is a large contraction on the underlying function space, while W is also causal and satisfies some extra conditions. We shall consider first the neutral functional differential equation (25.1) on the space C([0,T], ℝ n ), consisting of continuous maps from [0,T] into ℝ n , with the supremum norm.

Keywords: Global Existence; Operator Versus; Extra Condition; Supremum Norm; Neutral Equation (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0111-3_25

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DOI: 10.1007/978-1-4612-0111-3_25

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