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whereλ is a real parameter; q(t) is a real-valued function; ai , ai , bi, bi ∈ R, i = 0,1. Also we assume that q(t) is continuous, its differentiation exists and is integrable. This problem differs from the usual regular Sturm-Liouvill e problem in the sense that eigenvalue parameter λ is contained in the boundary condition at a. Problems of this type arise from the method of separation of variables applied to mathem atical models for certain physical problems including heat conduction and wave propagation, etc. [ 8]. It is shown by Walter [ 15] that this problem is self-adjoint problem . The purpose of this paper is to obtain asymptotic approximation s f r the eigenvalues of ( 1)-(3).

Asymptotics of eigenvalues for Sturm-Liouville problem with eigenparameter-dependent boundary conditions