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

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.
E-mail: aryanmath76@yahoo.com, aryan.mohammed@univsul.edu.iq






Article info

Original: 15 June.  2015

Revised: 20 August. 2015

Accepted: 30 August. 2015

Published online:  20 March. 2016





Key Words:

Eigenparameters,
eigenfunctions,
boundary conditions,
asymptotic behavior.


Abstract

In this work, we derived the general solution for nth order linear ordinary differential
equations of the form 􀀁(􀀃)(􀀅) + 􀀇􀀃 􀀁(􀀅) = 􀀊(􀀁), 􀀅 ∈ [􀀎, 􀀏]for 􀀇 ≠ 0, where m(y) =
−􀀚􀀛(􀀅)􀀁(􀀃􀀜􀀛)(􀀅) − ⋯ − 􀀚􀀃(􀀅)􀀁(􀀅), and 􀀚􀀛(􀀅), … , 􀀚􀀃(􀀅) are continuous functions of
􀀅 in the interval [􀀎, 􀀏] , 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.



Ċ
Ramyar Abdolrahman Taimur Ismail,
Apr 7, 2016, 2:52 AM