On singular boundary value problems for a second-order linear functional-differential equation (Q1588993)

Consider the equation \(\pi(t)\ddot x(t)- (Tx)(t)= f(t)\), \(t\in [0,1]\), with a linear bounded operator \(T\) of the space of continuous functions on \([0,1]\) into the space of summable functions on \([0,1]\). The authors establish sufficient conditions for the monotonicity of Green's operators of certain boundary value problems for \(\pi(t)= t\) or \(\pi(t)= 1-t\) or \(\pi(t)= t(1- t)\).