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MULTIPLICITY OF POSITIVE SOLUTIONS FOR HIGHER ORDER STURM-LIOUVILLE PROBLEMS
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Journal Article
MULTIPLICITY OF POSITIVE SOLUTIONS FOR HIGHER ORDER STURM-LIOUVILLE PROBLEMS
2001
Overview
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(2i+1)(0) = 0, 0 ≤ i ≤ m - 1, γy(2i)(1) - δy(2i+1)(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.
Publisher
The Rocky Mountain Mathematics Consortium,Rocky Mountain Mathematics Consortium
Subject
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