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Fourth Mississippi State Conference on Differential Equations and Computational Simulations
May 21-22, 1999
Mississippi State University and Electronic Journal of Differential Equations
Starkville, MS, USA

Organizers
Ratnasingham Shivaji, Bharat Soni, Jianping Zhu (Program Chair)

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Multiplicity of Positive Solutions for Higher Order Sturm-Liouville Problems
by
John M. Davis
Auburn University
Coauthors: Lynn H. Erbe, Johnny Henderson

We establish the existence of an arbitrary number of positive solutions to the 2mth order Sturm-Liouville type problem
(-1)m y(2m)(t) = f(t, y(t)),    0 <= t <= 1,

\alphay(2i)(0)-\betay(2i+1)(0)=0,    0 <= i <= m-1,

\gammay(2i)(1)+\deltay(2i+1)(1)=0,    0 <= i <= m-1,
where f:[0, 1]×[0, 1] --> [0, \infty) 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.

John Davis's Homepage

Date received: March 23, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacr-17.