Abstract
In this paper, our main aim is to investigate the spectral properties of a singular dissipative fourth order boundary value problem in lim-4 case with finite transmission conditions. For this purpose we construct a suitable differential operator in an appropriate Hilbert space. After showing that this differential operator is a dissipative operator we pass to the resolvent operator with an explicit form. Using this resolvent operator and Krein’s theorem we prove a completeness theorem on the boundary value transmission problem.
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Uğurlu, E., Bairamov, E. On the rate of the convergence of the characteristic values of an integral operator associated with a dissipative fourth order differential operator in lim-4 case with finite transmission conditions. J Math Chem 52, 2627–2644 (2014). https://doi.org/10.1007/s10910-014-0404-3
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DOI: https://doi.org/10.1007/s10910-014-0404-3