Literature cited
F. S. Rofe-Beketov, “Self-adjoint extensions of differential operators in spaces of vector-functions,” Teor. Funktsii, Punkts, Analiz Prilozhen., No. 8, 3–24 (1969).
M. L. Gorbachuk, “Self-adjoint boundary-value problems for second-order differential equations with unbounded operator coefficients,” Funkts. Anal. Prilozhen.,5, No. 1, 10–21 (1971).
L. I. Vainerman, “Dissipative boundary-value problems for second-order differential equations with unbounded variable operator coefficients,” Ukr. Mat. Zh.,24, No. 4, 530–534 (1974).
L. I. Vainerman, “Degenerate second-order elliptic equations in Hilbert space,” Differents. Uravn.,14, No. 3, 482–491 (1978).
S. G. Krein, Linear Differential Equations in Banach Spaces, Amer. Math. Soc. (1972).
Yu. M. Berezanskii, Eigenfunction Decomposition of Self-Adjoint Operators fin Russianl, Naukova Dumka, Kiev (1965).
V. I. Gorbachuk and M. L. Gorbachuk, “Some questions of the spectral theory of second-order linear differential equations with unbounded operator coefficients,” Ukr. Mat. Zh.,23, No. 1, 3–15 (1971).
G. N. Watson, Theory of Bessel Functions, Cambridge Univ. Press.
G. I. Laptev, “Strongly elliptic second-order equations in Hilbert spaces,” Liet. Mat. Rinkinys,8, No. 1, 87–99 (1968).
J. L. Lions, “Theoremes de traces et d'interpolation,” Ann. Sc. Norm. Sup. Pisa, Ser. 3,13, 389–403 (1959).
J. L. Lions and J. Peetre, “Sur une classe d'espaces d'interpolation,” Inst. Hautes Etudes Sci. Publ. Math.,19, 5–68 (1964).
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary-Value Problems and Applications, Springer-Verlag (1972).
M. L. Gorbachuk, A. N. Kochubei, and M. A. Rybak, “Dissipative extensions of differential operators in spaces of vector-functions,” in: Applications of Functional Analysis to Problems of Mathematical Physics [in Russian], Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev (1973), pp. 56–82.
G. I. Laptev, “Problems on eigenvalues for second-order differential equations in Banach and Hilbert spaces,” Differents. Uravn.,11, No. 9, 1151–1160 (1966).
L. I. Vainerman, “Second-order elliptic equations with degenerate unbounded operator coefficients,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 3, 195–197 (1977).
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Translated from Ukrainskii Matematieheskii Zhurnal, Vol. 31, No. 3, pp. 247–255, May–June, 1979.
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Vainerman, L.I. A degenerate elliptic equation with variable operator coefficients. Ukr Math J 31, 191–197 (1979). https://doi.org/10.1007/BF01089017
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DOI: https://doi.org/10.1007/BF01089017