On a nonlocal boundary value problem for second order linear ordinary differential equations (Q1900397)

This paper is concerned with existence and uniqueness theorems for the nonlocal boundary value problem \[ u'' = p_1(t)u + p_2 (t)u' + p_0(t), \quad u(a+) = c_1, \quad u(b-) = \int^b_a u(x)d \mu (x) + c_2. \tag{*} \] Here \(\mu : [a,b] \to R\) is a function of bounded variation and \(p_i(t) : (a,b) \to R\) are locally integrable only (therefore, BVP (*) includes also the singular case). The author establishes various sufficient conditions for the solvability of (*).