Delay differential equations with differentiable solution operators on open domains in C((-∞,0],ℝⁿ), and processes for Volterra integro-differential equations

2018/01/28 by Walther, Hans-Otto
#34 K 05 #37 L 05 #45 D 99 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.09214

Abstract

For autonomous delay differential equations x'(t)=f(x_t) we construct a continuous semiflow of continuously differentiable solution operators x₀↦ x_t, t≥0, on open subsets of the Fréchet space C((-∞,0],ℝⁿ). For nonautonomous equations this yields a continuous process of differentiable solution operators. As an application we obtain processes which incorporate all solutions of Volterra integro-differential equations x'(t)=∫₀^tk(t,s)h(x(s))ds

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