| Popis: |
For autonomous delay differential equations x ' ( t ) = f ( x t ) {x'(t)=f(x_t)} we construct a continuous semiflow of continuously differentiable solution operators x 0 → x t {x_0 \to x_t} , t ≤ 0 {t \le 0} , on open subsets of the Fre´chet space C ( ( - ∞ , 0 ] , R n ) {C((-\infty, 0], R^n)} . 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 t k ( t , s ) h ( x ( s ) ) d s {x'(t)={\int_0}^t k(t,s) h(x(s)) ds} . |
