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Volume 5, Number 1, 2015, Pages 146-158                                                                DOI:10.11948/2015013
The eigenvalue problem for elliptic partial differential equation with multi-point nonlocal conditions
Ahmed Elsaid,Shaimaa Helal,Ahmed El-Sayed
Keywords:Elliptic partial differential equation
Abstract:
      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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