On Two-point Boundary Value Problems for Higher Order Singular Ordinary Differential Equations

is integrable in the first argument on [a + ε, b − ε] for arbitrary ρ ∈ [0,+∞[ and ε ∈ ]0, (b− a)/2[ . Of special interest for us is the case where the function f (and therefore the function f) is non-integrable in the first argument on [a, b], having singularities at the ends of this segment. In this sense the problems (1), (2) and (1), (3) are singular ones. Singular boundary value problems for ordinary differential equations (including the problems (1), (2) and (1), (3)) have been intensively studied from the 60s of the last century up to the present time (see, e.g., [1]–[19] and the references cited therein). In [11], the problems (1), (2) and (1), (3) are studied in the case where the function f admits the one-sided estimate