The Eigenvalue Problem for Elliptic Partial Differential Equation With Two-Point Nonlocal Conditions

On Some Spectral Properties of a Nonlocal Boundary Value Problem A. M. A. El-Sayed, Zaki. F. A. El-Raheem and N. A. O. Buhalima

“…In this work we study the existence of at least one solution for the nonlocal boundary value problem of the second-order differential equation ( 1) and (2).…”

“…Nonlocal boundary value problems were first considered by Bitsadze and Samarskii [1] and later by Il'in and Moiseev [8], [9]. We refer the reader to ( [2], [3] and [12]) for recent results of nonlocal boundary value problems. It is well-known that many topics in mathematical physics require the investigation of the eigenvalues and eigenfunctions of Sturm-Liouville type boundary value problems.…”

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

“…By the same way we can prove the following lemma lemma 2. 4 The eigenfunctions that corresponds to two different eigenvalues of the non-local boundary value problem ( 1) and ( 3) are orthogonal.…”