IJPAM: Volume 112, No. 1 (2017)

Title

EIGENVALUES AND EIGENFUNCTIONS FOR REGULAR
STURM-LIOUVILLE EQUATION WITH NON-LOCAL
BOUNDARY CONDITIONS

Authors

A.M.A. El-Sayed$^1$, F.A.Z. EL-Raheem$^2$, A.O.N. Buhalima$^3$
$^1$Faculty of Science
Alexandria University
Alexandria, EGYPT
$^2$Faculty of Education
Alexandria University
Alexandria, EGYPT
$^3$Faculty of Science
Omar AlMukhtar University
Albeda, LIBYA

Abstract

In this paper, we study the existence and some general properties of eigenvalues and eigenfunctions of a nonlocal boundary value problem of the Sturm-Liouville differential equation.

History

Received: August 28, 2016
Revised: October 23, 2016
Published: January 26, 2017

AMS Classification, Key Words

AMS Subject Classification: 34A55, 34B10, 34B15, 34B18, 34L10, 34L40, 34K10
Key Words and Phrases: Sturm-Liouville boundary value problem, nonlocal condition, eigenvalues, eigenfunctions

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
A. V. Bitsadze and A. A. Samarskii, Some elementary generalizations of linear elliptic boundary value problems, Dokl. Akad. Nauk SSSR, 185 (1969), 739-740.

2
A. M. Nakhushev, Equations of Mathematical Biology, Vysshaya Shkola, Moscow, 1995, In Russian.

3
A. M. A. El-Sayed, E. M. Hamdallah, Kh. W. Elkadeky, Solution of a class of internal nonlocal Cauchy problems for the differential equation $x'(t) = f(t, x(t), x'(t))$, Fixed Piont Theorem, 15, No. 2 (2014), 441-448.

4
A. M. A. EL-Sayed, M. S. EL-Azab, A. Elsaid and S. M. Helal, Eigenvalue problem for Elliptic partial differential equations with nonlocal boudary conditions, Journal of Fractional Calculus and Applications, 5(3S), No. 14 (2014), 1-11.

5
A. M. A. EL-Sayed and F. M. Gaafar, Stability of a nonlinear non-autonomous fractional order systems with different delays and non-local conditions, Advances in Difference Equations (2011), doi: https://doi.org/10.1186/1687-1847-2011-47.

6
A. M. A. EL-Sayed, Z. F. A. EL-Raheem AND N. A. O. Buhalima, Eigenvalues and eigenfunctions of non-local boundary value problems of the Sturm-Liouville equation, Electronic Journal of Mathematical Analysis and Applications, 5, No. 1 (2017), 179-186.

7
G. Freiling, V. Yurko, Inverse Sturm-Liouville Problems and their Applications, Nova Science, New York, 2001.

8
K. Schuegerl. Bioreaction Engineering, Reactions Involving Microorganisms and Cells, 1, John Wiley and Sons, 1987.

9
N. I. Ionkin. The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition, Differ. Equ., 13, No. 2 (1977), 294-304, In Russian.

How to Cite?

DOI: 10.12732/ijpam.v112i1.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 112
Issue: 1
Pages: 103 - 113


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).