Solvability of a two-point boundary-value problem for a linear singular functional differential equation (Q2276607)

Let \(T: C[a, b]\to L[a, b]\) be a linear and bounded operator. The author gives conditions on the operator \(T\) which guarantee that the singular Dirichlet boundary value problem \[ (t- a)^{\mu_1}(b- t)^{\mu_2} x''(t)= (Tx)(t)+ f(t),\quad x(a)= 0,\quad x(b)= 0, \] has a unique solution \(x\) satisfying the inequality \(x< 0\) on \((a, b)\) for any nonnegative \(f\in L[a, b]\), \(f\not\equiv 0\). This paper supplements the results of the author's previous paper [Izv. Vyssh. Uchebn. Zaved., Mat. 45, No. 6, 12-22 (2001; Zbl 1008.34019).