Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions
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Date
2019-08-01
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Ankara Üniversitesi Fen Fakültesi
Abstract
In this paper, we consider the operator L generated in L₂(R₊) by the differential expression
l(y)=-y′′+q(x)y,x∈R₊:=[0,∞)
and the boundary condition
((y′(0))/(y(0)))=α₀+α₁λ+α₂λ²,
where q is a complex valued function and α_{i}∈C,[mbox]<LaTeX>\mbox{\:}</LaTeX>i=0,1,2α₂. We have proved that spectral expansion of L in terms of the principal functions under the condition
q∈AC(R₊), lim_{x→∞}q(x)=0, sup[e^{ε√x}|q′(x)|]<∞, ε>0
taking into account the spectral singularities. We have also proved the convergence of the spectral expansion.
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Keywords
Eigenvalues, Spectral singularities, Principal functions