THE EIGENVALUE PROBLEM FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATION WITH TWO-POINT NONLOCAL CONDITIONS | Zendy

A. Elsaid | Zendy; S.M. Helal | Zendy; A. M. A. ElSayed | Zendy

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THE EIGENVALUE PROBLEM FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATION WITH TWO-POINT NONLOCAL CONDITIONS

Author(s) -

A. Elsaid,

S.M. Helal,

A. M. A. ElSayed

Publication year - 2015

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2015013

Subject(s) - eigenvalues and eigenvectors , mathematics , mathematical analysis , partial differential equation , matrix differential equation , elliptic partial differential equation , differential equation , matrix (chemical analysis) , physics , quantum mechanics , materials science , composite material

We study the spectral problem for the system of difference equations of a two-dimensional elliptic partial differential equation with nonlocal conditions. A new form of two-point nonlocal conditions that involve interior points is proposed. The matrix of the difference system is nonsymmetric thus different types of eigenvalues occur. The conditions for the existence of the eigenvalues and their corresponding eigenvectors are presented for the one dimensional problem. Then, these relations are generalized to the two-dimensional problem by the separation of variables technique.

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