EXISTENCE OF POSITIVE SOLUTIONS OF A HIGHER ORDER NONLOCAL SINGULAR BOUNDARY VALUE PROBLEM
by
John R. Graef
University of Tennessee at Chattanooga
Coauthors: Johnny Henderson and Bo Yang

The authors consider the nonlocal singular boundary value problem

y(n) = f(x, y),     0 < x < 1,    y(i-1)(0) = 0,     i = 1, 2, ..., n-2,    y(n-2)(p) = 0,     ó õ 1 q  w(x) y(n-1)(x) dx = 0,

where 1/2 < p < q < 1, and f(x, y) is singular at x=0, y=0, and possibly at y=∞ in the sense that f may vanish at y=∞. Here, f(x, y) is decreasing in y and w is continuous and nondecreasing with w(x) > 0 on (q, 1]. The proof makes use of the Gatica-Oliker-Waltman fixed point theorem in a cone.

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Date received: February 14, 2008