Singular Conjugate Boundary Value Problems on a Time Scale

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: Let T₁ be a time scale symmetric about 1/2. Let 1/2 ÎT₁ be right dense and define T = T₁ Ç [0,1]. The conjugate nonlinear boundary value problem,

- u^DD (t) = a (t) f (u (t)), t Î T \ {0, 1}
u(0) = u(1) = 0, where a (t) is singular at t = 1/2 and f satisfies certain growth conditions, is shown to have infinitely many solutions using Krasnosel'skii's fixed point theorem.

1991 AMS (MOS) Subject Classification: 34B15, 34B16, 34B18, 34G20.

KEYWORDS: Conjugate boundary value problem, time scale, Green's function, multiple solutions.

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