Solution of a semilinear differential-functional equation with infinite delay in a Banach space
From author's abstract: ``This paper is concerned with the existence of solutions to the initial value problem for a semilinear functional-differential equation with infinite delay in a Banach space \[ x'(t)= Lx_t+ f(t, x_t),\quad t\in[0,a] (a>0),\quad x(t)= \varphi(t),\quad t\in]-\infty, 0]. \] The result is based on the Leray-Schauder alternative and a priori bounds on solutions''.
semilinear functional-differential equation
scientific article; zbMATH DE number 1347402