FOCAL BOUNDARY VALUE PROBLEMS FOR SINGULAR DIFFERENCE EQUATIONS

Johnny Henderson, Department of Mathematics, Baylor University, Waco, Texas 76798-7328, Johnny_Henderson@baylor.edu.

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

Computers and Mathematics with Applications, 36 (1998), No. 10-12, 1 - 10.

ABSTRACT: Solutions are shown to exist for the boundary value problem Dⁿ u(m) + f (m, u, D u, …, D^n-2 u) = 0, m Î {0, …, T } satisfying focal boundary conditions, where f (m, y₁, …, y_n-1) is singular at y_i = 0, i = 1, …, n. The techniques involve concavity properties, iterations, and a fixed point theorem for mappings which are decreasing with respect to a cone in a Banach space.

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