A survey on stationary problems, Green’s functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions∗

In the theory of differential equations, the basic concepts have been formulated studying the problems of classical mathematical physics. However, the modern problems motivate to formulate and investigate the new ones, for example, a class of nonlocal problems. Nonlocal conditions arise when we cannot measure data directly at the boundary. In this case, the problem is formulated, where the value of the solution and/or a derivative is linked to a few points or the whole interval. A review on differential equations with more general boundary conditions (BC) involving also Stieltjes measures has been written by Whyburn [232]. In 1963, Cannon [26] formulated new problem with BCs, which are now called nonlocal. The term “nonlocal boundary value problem” most likely to have been used by Beals in 1964 [12, 13]. He investigated elliptic type differential equations with nonclassical BCs. A parabolic problem with integral boundary condition