John M. Davis, Paul W. Eloe, John R. Graef, Johnny Henderson
Department of Mathematics
Baylor University
Waco, Texas, 76798-7328, USA
Department of Mathematics
University of Dayton
300 College Park, Dayton, Ohio, 45469-2317, USA
Department of Mathematics
The University of Tennessee at Chattanooga
Chattanooga, Tennessee, 37403, USA
e-mail: John-Graef@utc.edu

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

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