References
I. G. Petrovskiî, “On the Cauchy problem for a system of linear partial differential equations involving nonanalytic functions,” Byul. Moskov. Univ. Sekts. A,1, No. 7, 1–72 (1938).
I. M. Gel'fand and G. E. Shilov, Certain Problems of the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).
A. Kh. Mamyan, “General boundary-value problems in a layer,” Dokl. Akad. Nauk SSSR,267, No. 2, 293–296 (1982).
A. A. Samarskiî, “On some problems of the theory of differential equations,” Differentsial'nye Uravneniya,16, No. 11, 1925–1935 (1980).
A. M. Nakhushev, “On nonlocal problems with a shift and their relations with loaded equations,” Differentsial'nye Uravneniya,21, No. 1, 95–101 (1985).
V. M. Borok, “A criterion for absolutec-stability of partial differential equations,” Differentsial'nye Uravneniya,24, No. 3, 438–444 (1988).
B. I. Ptashnik, Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
A. A. Makarov, “On necessary and sufficient conditions for well-posedness of a boundary-value problem in a layer for a system of partial differential equations,” Differentsial'nye Uravneniya,17, No. 2, 320–324 (1981).
L. V. Fardigola, “Well-posed problems in a layer with differential operators in a boundary condition,” Ukrain. Mat. Zh.,44, No. 8, 1083–1090 (1992).
A. Seidenberg, “A new decision method for elementary algebra,” Ann. of Math. (2),60, No. 2, 365–374 (1954).
L. Hörmander, The Analysis of Linear Partial Differential Operators. Vol. 2: Pseudodifferential Operators [Russian translation], Mir, Moscow (1986).
H. Whitney, “Elementary structure of real algebraic varieties,” Ann. of Math. (2),66, No. 3, 545–556 (1957).
A. G. Khovanskiî, “On a class of simultaneous transcendental equations,” Dokl. Akad. Nauk SSSR,255, No. 4, 804–807 (1980).
S. Lojasiewicz, “Division d'une distribution par une fonction analytique des variables réelles,” C. R. Acad. Sci. Paris,246, No. 5, 683–686 (1958).
L. Hörmander, “On the division of distributions by polynomials,” Ark. Mat.,3, No. 6, 555–558 (1958).
I. L. Vilents, A Boundary-Value Problem for an Evolution System of Partial Differential Equations in a Topological Vector Space [Preprint] [in Russian], Fiziko-Tekhnicheskiî Instiut Nizkikh Temperatur Akad. Nauk USSR, Khar'kov (1979).
L. V. Fardigola, “A nonlocal boundary-value problem in a layer: Influence of parameters on the properties of solutions,” Differentsial'nye Uravneniya,27, No. 12, 2151–2161 (1991).
Additional information
Khar'kov. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 2, pp. 424–438, March–April, 1997.
Translated by Yu. A. Dmitrieva
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Fardigola, L.V. On a two-point nonlocal boundary value problem in a layer for an equation with variable coefficients. Sib Math J 38, 367–379 (1997). https://doi.org/10.1007/BF02674636
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DOI: https://doi.org/10.1007/BF02674636