Correct solvability of the Sturm–Liouville equation with delayed argument

Abstract

We consider the equation

Admissible spaces for a first order differential equation with delayed argument

“…Such an investigation is needed because this is the first time problem (i)-(ii) is being posed for equation (1.1) (for the second order equation the same question was studied in [2]). Indeed, to the best of our knowledge, for equations with delayed argument, initial and boundary-value problems on a finite segment or on a semi-axis have been studied (see [1], [3], [4], [6]).…”