NONLINEAR BOUNDARY VALUE PROBLEMS WITH MULTIPLE POSITIVE SOLUTIONS

We give conditions on f(y) which guarantee that the boundary value problem T(n)y(x) = f (y(x)), 0 < x < A, y((2j)) (0) = 0 = y((2j+1)) (A), j = 0,1, ... , n-1, where T-n is the nth iterate of the operator Ty(x) = -1/w(x) (P(x)Y'(x))', have a prescribed number of multiple positive solutions. Our main tool is a fixed point theorem of Krasnosel'skii.