On the Eigenvalue Accumulation of Sturm-Liouville Problems Depending Nonlinearly on the Spectral Parameter

A nonlinear spectral problem for a Sturm-Liouville equation-(p(x, λ)y'(x, λ))' + q(x, λ) y(x, λ) = 0 on a finite interval [a, b] with λ-dependent boundary conditions is considered. The spectral parameter λ is varying in an interval ∧ and p(x, λ), q(x, A) are real, continuous functions on [a, b] × ∧ Some criteria to the eigenvalue accumulation at the endpoints of A will be established. The results are applied to concrete problems arising in magnetohydrodynamics.