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Eigenvalue Approach to Even Order System Periodic Boundary Value Problems

  Published:2011-07-04
 Printed: Mar 2013
  • Qingkai Kong,
    Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA
  • Min Wang,
    Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA
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Abstract

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: Green's function, high order system boundary value problems, positive solutions, Sturm-Liouville problem Green's function, high order system boundary value problems, positive solutions, Sturm-Liouville problem
MSC Classifications: 34B18, 34B24 show english descriptions Positive solutions of nonlinear boundary value problems
Sturm-Liouville theory [See also 34Lxx]
34B18 - Positive solutions of nonlinear boundary value problems
34B24 - Sturm-Liouville theory [See also 34Lxx]
 

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