Abstract
In this work, we describe well-defined dissipative boundary conditions related with a singular third-order differential equation in lim-3 case at singular point. Using the characteristic function of the corresponding dissipative operator we introduce a completeness theorem.
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Gilbert, R.C.: The deficiency index of a third order operator. Pac. J. Math. 68, 369–392 (1977)
Gorbachuk, V.I., Gorbachuk, M.L.: Boundary Value Problems for Ordinary Differential Equations. Kluwer, Dordrecht (1991)
Goriunov, A.S., Mikhailets, V.A.: On extensions of symmetric quasidifferential operators of odd order. Dopov. NAS Ukr. 9, 27–31 (2009). (in Russian)
Hinton, D.B.: Deficiency indices of odd-order differential operators. Rocky Mt. J. Math. 8, 627–640 (1978)
Krein, M.G.: On the indeterminate case of Sturm–Liouville boundary problems in the interval \((0,\infty )\). Izv. Akad. Nauk SSSR Ser. Mat. 16, 293–324 (1952). (in Russian)
Kuzhel, A.: Characteristic Functions and Models of Nonself-Adjoint Operators. Kluwer Academic Publishers, Dordrecht (1996)
Naimark, M.A.: Linear Differential Operators, Part II, Linear Differential Operators in Hilbert Space. George G. Harrap and Company, London (1966)
Naimark, M.A.: Linear Differential Operators, Part I, Elementary Theory of Linear Differential Operators. George G. Harrap and Company, London (1968)
Preiffer, G.W.: Deficiency indices of a third-order equation. J. Differ. Equ. 11, 474–490 (1972)
Uğurlu, E.: Singular multiparameter dynamic equations with distributional potentials on time scales. Quaes. Math. 40, 1023–1040 (2017)
Uğurlu, E.: Regular third-order boundary value problems. Appl. Math. Comput. 343, 247–257 (2019)
Uğurlu, E.: Third-order boundary value transmission problems. Turk. J. Math. 43, 1518–1532 (2019)
Uğurlu, E.: Extensions of a minimal third-order formally symmetric operator. Bull. Malays. Math. Sci. Soc. 43, 453–470 (2020)
Uğurlu, E., Baleanu, D.: Coordinate-free approach for the model operator associate with a third-order dissipative operator. Front. Phys. (2019). https://doi.org/10.3389/fphy.2019.00099
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Communicated by Manuel D. Contreras.
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Uğurlu, E. Singular dissipative third-order operator and its characteristic function. Ann. Funct. Anal. 11, 799–814 (2020). https://doi.org/10.1007/s43034-020-00055-z
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DOI: https://doi.org/10.1007/s43034-020-00055-z