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Eigenvalue Approach to Even Order System Periodic Boundary Value Problems

Published online by Cambridge University Press:  20 November 2018

Qingkai Kong  and
Min Wang
Qingkai Kong
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA e-mail: kong@math.niu.edumwang@math.niu.edu
Min Wang
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA e-mail: kong@math.niu.edumwang@math.niu.edu
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Abstract

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We study an even order system boundary value problem with periodic boundary conditions. By establishing the existence of a positive eigenvalue of an associated linear system Sturm-Liouville problem, we obtain new conditions for the boundary value problem to have a positive solution. Our major tools are the Krein-Rutman theorem for linear spectra and the fixed point index theory for compact operators.

Keywords

34B1834B24Green's functionhigh order system boundary value problemspositive solutionsSturm-Liouville problem.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 1 , 01 March 2013 , pp. 102 - 115
Copyright
Copyright © Canadian Mathematical Society 2013

References

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