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,lam bda)y'(x,lambda))' + q(x,lambda)y(x,lambda) = 0 on a finite interval [ a, b] with lambda-dependent boundary conditions is considered. The spe ctral parameter lambda is varying in an interval Lambda and p(x, lambd a), q(x,lambda) are real, continuous functions on [a, b] x Lambda. Som e criteria to the eigenvalue accumulation at the endpoints of Lambda w ill be established. The results are applied to concrete problems ari s ing in magnetohydrodynamics.