IJPAM: Volume 109, No. 1 (2016)

POSITIVE SOLUTIONS FOR A SINGULAR FOURTH ORDER
NONLOCAL BOUNDARY VALUE PROBLEM

John M. Davis$^1$, Paul W. Eloe$^2$, John R. Graef$^3$, Johnny Henderson$^4$
$^{1,4}$Department of Mathematics
Baylor University
Waco, Texas, 76798-7328, USA
$^2$Department of Mathematics
University of Dayton
300 College Park, Dayton, Ohio, 45469-2317, USA
$^3$Department of Mathematics
The University of Tennessee at Chattanooga
Chattanooga, Tennessee, 37403, USA
e-mail: [email protected]


Abstract. Positive solutions are obtained for the fourth order nonlocal boundary value problem, u(4)=f(x,u), 0 < x < 1, u(0) = u''(0) = u'(1) = u''(1) - u''(2/3)=0, where f(x,u) is singular at x = 0, x=1, y=0, and may be singular at y=∞. The solutions are shown to exist at fixed points for an operator that is decreasing with respect to a cone.

Received: August 1, 2016

AMS Subject Classification: 34B16, 34B18, 34B10, 47H10

Key Words and Phrases: fixed point, nonlocal, boundary value problem, singular

Download paper from here.




DOI: 10.12732/ijpam.v109i1.6 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: 2016
Volume: 109
Issue: 1
Pages: 67 - 84


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

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