A SINGULAR SECOND ORDER BOUNDARY VALUE PROBLEM

Eric R. Kaufmann, Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, Arkansas 72204-1099, erkaufmann@ualr.edu.

Nickolai Kosmatov, Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, Arkansas 72204-1099, nxkosmatov@ualr.edu

Submitted.

ABSTRACT:We study the second order boundary value problem

- u'' = a (t) f (u (t) ),
a u(0) - b u'(0) = 0,
g u(1) + d u'(1) = 0,
where a (t) = Pi = 1n ai (t) and a, b, g, d > 0, a g + a d + b g > 0. We assume that each ai (t) Î L pi[0,1] for pi > 1 and that each ai (t) has a singularity in (0, 1). To show the existence of countably many positive solutions we apply Hölder's inequality and Krasnosel'skii's fixed point theorem for operators on a cone.

1991 AMS (MOS) Subject Classification: 34B16, 34B18, 34B27, 34G20.

KEYWORDS: Boundary value problem, fixed point theorem, Green's function, Hölder's inequality, multiple solutions.

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