A critical points approach to multiplicity results for multi-point boundary value problems

Abstract

In this article, we prove the existence of at least three classical solutions to the multi-point boundary value system

for i = 1, … , n. Our main tool is a recent three critical points theorem of B. Ricceri.

Keywords:

• three solutions
• critical point
• multi-point boundary value problem
• multiplicity results

AMS Subject Classifications::

• 34B10
• 34B15

Acknowledgments

The authors would like to thank the referee for a very careful reading of this manuscript and for making good suggestions for the improvement of this article. Research by S. Heidarkhani was supported in part by IPM Grant No. 89350020.