Multiplicity of positive solutions for higher order Sturm-Liouville problems

We establish the existence of an arbitrary number of positive solutions to the 2mth order Sturm-Liouville type problem (-1)(m)((2m))(y) (t) = f(t,y(t)), 0 less than or equal to t less than or equal to 1, alphay((2i))(0) - betay((2i+1))(0) = 0, 0 less than or equal to i less than or equal to m - 1, gammay((2i))(1) + deltay((2i+1))(1) = 0, 0 less than or equal to i less than or equal to m - 1, where f : [0, I] x [0, infinity) --> [0, infinity) is continuous. We accomplish this by making growth assumptions on f which we state in terms which generalize assumptions in recent works regarding superlinear and/or sublinear growth in f.