A nonlocal problem for a first-order partial differential equation

EIGENVALUES AND EIGENFUNCTIONS OF NON-LOCAL BOUNDARY VALUE PROBLEMS OF THE STURM-LIOUVILLE EQUATION Vol. 5(1) Jan. 2017, No. 18, pp. 179-186 A. M. A. EL-SAYED, Z. F. A. EL-RAHEEM AND N. A. O. BUHALIMA

“…The problems of differential equations with nonlocal conditions have been studied by some authors (see for example [1] and [3]- [5]). Also theoretical investigation of Sturm-Liouville boundary value problems with various types of nonlocal boundary conditions is a topical problem and recently has been paid much attention to them in the scientific literature (see for exampl [6] and [7] - [9]).…”

“…Also theoretical investigation of Sturm-Liouville boundary value problems with various types of nonlocal boundary conditions is a topical problem and recently has been paid much attention to them in the scientific literature (see for exampl [6] and [7] - [9]). Consider the two non-local boundary value problems of the Sturm-Liouville equation − y ′′ + q(x)y = λ 2 y, 0 ≤ x ≤ π (1) with each one of the two non-local conditions…”