... initial and boundary value problems singular in the dependent variable,” in Handbook of Differential Equations, pp 1–68, Elsevier/NorthHolland, Amsterdam, The Netherlands, 2004 15 M Cherpion and C ... of α and β and r ≤ x ≤ 1/r Therefore Theorem 5.4 implies the existence of a weak solution of 7.7 between α and β Moreover, since f is positive between α and β the solution is increasing and, ... Equations with Discontinuous Righthand Sides, vol 18 of Mathematics and Its Applications (Soviet Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988 11 S Heikkil¨ and V Lakshmikantham,...