### Eigenfunctions and asymptotic behavior of Eigenvalues to the given boundary value problem with Eigenparameter in the boundary conditions

Aryan Ali Mohammed
Department of Mathematics, School of Science, Faculty of Science and Science Education, University of Sulaimani, Sulaimanyah,
Iraq.

Abstract

In this work, we derived the general solution for nth order linear ordinary differential
equations of the form for and are continuous functions of via the method of variation of
parameters. Likewise we found the eigenfunctions for the given second boundary value
problem [1]-[3] as well as the boundedness of eigenfunctions, and the sign of real part of
the eigenvalues have been specified through the sign of one parameter in the boundary
conditions. Finally, the asymptotic behavior of eigenvalues to the given problem was
studied.

Key Words:
Eigenparameters, eigenfunctions, boundary conditions, asymptotic behavior.

References

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