We discuss, via a version of the Birkhoff-Kellogg theorem, the existence of positive and negative eigenvalues of Hammerstein integral equations with sign-changing nonlinearities and functional terms. The corresponding eigenfunctions have a given norm that, in turn, provides a location for the eigenvalues. As an application, we study the solvability of parameter-dependent boundary value problems for nonlocal ordinary differential equations. Two examples illustrate the applicability of the theory in the case of mixed and Dirichlet boundary conditions.
Infante et al. (Wed,) studied this question.
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