A Multiplicity Result for a Boundary Value Problem with Infinitely Many Singularities

A MULTIPLICITY RESULT FOR A BOUNDARY VALUE PROBLEM WITH INFINITELY MANY SINGULARITIES

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

Journal Mathematical Analysis Application, 269 (2002), 444 - 453.

ABSTRACT: We consider the second order boundary value problem

-u''(t) = a(t) f(u(t)), 0 < t < 1,

u(0) = u(1) = 0,

where a(t) Î L^p[0,1] for some p > 1 and has countably many singularities in [0, 1/2). We show that there exist countably many positive solutions using Hölder's inequality and Krasnosel'skií's fixed point theorem for operators on a cone.

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

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

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