The spectrum of eigenparameter-dependent discrete Sturm-Liouville equations

作者：Bairamov Elgiz^*; Aygar Yelda; Koprubasi Turhan

来源：Journal of Computational and Applied Mathematics, 2011, 235(16): 4519-4523.

DOI：10.1016/j.cam.2009.12.037

• Discrete equations
• Spectral analysis
• Eigenvalues
• Spectral singularities

Let us consider the boundary value problem (BVP) for the discrete Sturm-Liouville equation
a(n-1)y(n-1) + b(n)y(n) + a(n)y(n+1) = lambda y(n), n is an element of N, (0.1)
(gamma(0) + gamma(1)lambda)y(1) + (beta(0) + beta(1)lambda)y(0) = 0, (0.2)
where (a(n)) and (b(n)), n is an element of N are complex sequences, gamma(i), beta(i) is an element of C, i = 0, 1, and lambda is a eigenparameter. Discussing the point spectrum, we prove that the BVP (0.1), (0.2) has a finite number of eigenvalues and spectral singularities with a finite multiplicities, if
sup(n is an element of N) [exp(epsilon n(delta)) (vertical bar 1 - a(n)vertical bar + vertical bar b(n)vertical bar)] < infinity,
for some epsilon > 0 and 1/2 <= delta <= 1.

• 出版日期2011-6-15