Abstract
We establish the existence of an arbitrary number of positive solutions to the 2mth order Sturm-Liouville type problem (−1)my(2m)(t) = f(t, y(t)), 0 ≤ t ≤ 1, αy(2i)(0)− βy(0) = 0, 0 ≤ i ≤ m− 1, γy(1) + δy(1) = 0, 0 ≤ i ≤ m− 1, where f : [0, 1]×[0,∞) → [0,∞) 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 .
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