Eigenvalue Approach to Even Order System Periodic Boundary Value Problems

Abstract

AbstractWe study an even order systemboundary value problemwith 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