Cilt:68 Sayı:02 (2019)

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Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions
(Ankara Üniversitesi Fen Fakültesi, 2019-08-01) Yokuş, Nihal; Arpat, Esra Kır; Other; Other
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]\mbox{\:}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.