Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications

Let be an integer and . We show the existence of the principal eigenvalues of linear periodic eigenvalue problem , and we determine the sign of the corresponding eigenfunctions, where is a parameter, and in , and the weight function changes its sign in . As an application of our spectrum results, we use the global bifurcation theory to study the existence of positive solutions for the corresponding nonlinear problem.

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