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On the eigenvalue accumulation of Sturm-Liouville problems depending nonlinearly on the spectral parameter. (English) Zbl 0892.34019

The paper deals with the equation

-(p(x,λ)y ' (x,λ)) ' +q(x,λ)y(x,λ)=0

on [a,b], with λ-dependent Sturm-Liouville boundary conditions, where λ varies in a finite or infinite interval Λ. The authors obtain criteria for the eigenvalue accumulation at the endpoints of Λ. Applications to some concrete problems arising in magnetohydrodynamics are given.

34B24Sturm-Liouville theory
76W05Magnetohydrodynamics and electrohydrodynamics
34B15Nonlinear boundary value problems for ODE
34L20Asymptotic distribution of eigenvalues for OD operators