MULTIPLE POSITIVE SOLUTIONS FOR HIGHER ORDER BOUNDARY VALUE PROBLEMS

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

Rocky Mountain Journal of Mathematics, 28 (1998), No. 3, 1017-1028.

ABSTRACT: Multiple positive solutions are shown to exist for the boundary value problem

u (n) + f (t, u) = 0,
a u (n - 2)(0) - b u (n - 1)(0) = 0,
g u (n - 2)(1) + d u (n - 1)(1) = 0,
u (i) (0) = 0, 0 < i < n - 3,
when f is sublinear at one end point (zero or infinity) and superlinear at the other. The methods involve applications of a fixed point theorem for operators on a cone in a Banach space.

AMS (MOS) subject classification 34B15, 34B27.

Keywords: Boundary value problems, cones in a Banach space, Green's functions, positive solutions.

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