Yokuş, NihalArpat, Esra Kir2019-12-062019-12-062019Yokuş, N., Kır, A. E. (2019). Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions. Communications Faculty of Science University of Ankara Series A1mathematics and Statistics, 68, 2, 1316-1334.1303-5991https://dx.doi.org/10.31801/cfsuasmas.526270https://hdl.handle.net/11492/2520WOS:000488869500008In this paper, we consider the operator L generated in L-2 (R+) by the differential expression l(y) = -y '' + q(x)y, x is an element of R+ := [0, infinity) and the boundary condition y'(0)/y(0) = alpha(0) +alpha(1)lambda +alpha(2)lambda(2), where q is a complex valued function and alpha(i) is an element of C, i = 0, 1, 2 with alpha(2) not equal 0. We have proved that spectral expansion of L in terms of the principal functions under the condition q is an element of AC(R+), lim(x ->infinity) q(x) = 0, sup(x is an element of R+) [e(epsilon root x)vertical bar q' (x)vertical bar] < infinity, epsilon > 0 taking into account the spectral singularities. We have also proved the convergence of the spectral expansion.enEigenvaluesSpectral SingularitiesPrincipal FunctionsResolventSpectral ExpansionArticle68213161334info:eu-repo/semantics/openAccess378279WOS:00048886950000810.31801/cfsuasmas.526270N/A