Abstract
We establish differential properties of generalized solutions of multipoint boundary-value problems for ordinary differential equations.
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REFERENCES
S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Leningrad University, Leningrad (1950).
T. I. Zelenyak, “On one class of boundary-value problems,” in: “Mathematical Models and Methods for Their Investigation” [in Russian], Vol. 1, Krasnoyarsk (2001), pp. 264–267.
T. I. Zelenyak and B. I. Golets, “On some boundary-value problems,” in: “Mathematical Models and Methods for Their Investigation” [in Russian], Krasnoyarsk (1999).
Yu. N. Valitsky, “Multipoint problem for a differential equation in the Hilbert space,” J. Inver. Ill-Posed Probl., 2, No. 4, 327–347 (1994).
S. A. Abdo and N. I. Yurchuk, “Multipoint boundary-value problems for certain differential-operator equations. I. A priori estimates,” Differents. Uravn., 21, No. 3, 417–425 (1985).
S. A. Abdo and N. I. Yurchuk, “Multipoint boundary-value problems for certain differential-operator equations. II. Solvability and properties of solutions,” Differents. Uravn., 21, No. 5, 806–815 (1985).
T. I. Zelenyak, “On localization of eigenvalues of a spectral problem,” Sib. Mat. Zh., 30, No. 4, 53–61 (1989).
Yu. V. Pokornyi, “On some estimates of the Green function of a multipoint boundary-value problem,” Mat. Zametki, 4, No. 6, 533–540 (1968).
B. I. Ptashnik, Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
A. L. Teptin, “On a multipoint boundary-value problem whose Green function changes its sign in “chess” order,” Differents. Uravn., 20, No. 11, 1910–1911 (1984).
F. R. Gantmakher and M. G. Krein, Oscillating Matrices and Kernels and Small Oscillations of Mechanical Systems [in Russian], Gostekhteorizdat, Moscow (1950).
M. Sh. Birman, “On the theory of self-adjoint extensions of positive-definite operators,” Mat. Sb., 38 (80), No. 4, 431–450 (1956).
K. Friedrichs, “Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren,” Math. Ann., 109, 465–487 (1934).
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Valitskii, Y.N., Golets, B.I. & Zelenyak, T.I. Multipoint Boundary Conditions for Differential Operators. Ukrainian Mathematical Journal 55, 157–163 (2003). https://doi.org/10.1023/A:1025085021869
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DOI: https://doi.org/10.1023/A:1025085021869