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Multipoint nonlocal problem for factorized equation with dependent coefficients in conditions. (English) Zbl 1326.35080
Summary: The conditions of correct solvability of multipoint nonlocal problem for factorized PDE with coefficients in conditions, which depends on one real parameter, is established. It is shown that these conditions on the set of full Lebesgue measure of the interval parameters are fulfilled.

35G15 Boundary value problems for linear higher-order PDEs
11K60 Diophantine approximation in probabilistic number theory
Full Text: DOI
[1] Gorodetskii V.V., Drin’ Ya.M. Nonlocal multipoint with respect to time problem for evolution pseudo-differential equations in spaces of periodic functions. Bukovyna Math. J. 2014, 2 (1), 26-42. (in Ukrainian) · Zbl 1313.47172
[2] Il’kiv V.S. Multipoint nonlocal boundary value problem for a system of nonhomogeneous partial differential equations with time variable continuous coefficients. Math. Bull. Shevchenko Sci. Soc. 2004, 1, 47-58. (in Ukrainian)
[3] Il’kiv V.S. The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations. Carpathian Math. Publ. 2009, 1 (1), 47-58. (in Ukrainian)
[4] Il’kiv V.S. Time-Variable Extension of the Solution of a Nonlocal Multipoint Problem for Partial Differential Equations with Constant Coefficients. J. Math. Sci. 2001, 107 (1), 3615-3619. doi: 10.1023/A:1011954509838 (translation of Mat. Metodi Fiz.-Mekh. Polya 1998, 41 (4), 78-82. (in Ukrainian)) · doi:10.1023/A:1011954509838
[5] Il’kiv V.S., Ptashnyk B.I. Problems for partial differential equations with nonlocal conditions. Metric approach to the problem of small denominators. Ukrainian Math. J. 2006, 58 (12), 1847-1875. doi: 10.1007/s11253-006-0172-8 (translation of Ukrain. Mat. Zh. 2006, 58 (12), 1624-1650. (in Ukrainian)) · Zbl 1114.35001 · doi:10.1007/s11253-006-0172-8
[6] Il’kiv V.S., Maherovska T.V. Boundary-value problem with non-local multipoint conditions for hyperbolic equation. Math. Methodi Fiz.-Mekh. Polya 2007, 50 (3), 66-81. (in Ukrainian)
[7] Il’kiv V.S., Maherovska T.V. Nonlocal multi-point problem for high order strong hyperbolic equation. Math. Bull. Shevchenko Sci. Soc. 2007, 4, 107-115. (in Ukrainian)
[8] Martynyuk O.V. The multipoint problem for one class of differential-operational equations. Dopov. Nats. Akad. Nauk Ukr. 2011, 10, 19-24. (in Ukrainian) · Zbl 1249.34170
[9] Martynyuk O.V., Gorodetskii V.V. Multipoint problem for a class of evolution equations. Differ. Equ. 2013, 49 (8), 975-985. doi: 10.1134/S0012266113080065 (translation of Differ. Uravn. 2013, 49 (8), 1005-1015. (in Russian)) · Zbl 1282.35214 · doi:10.1134/S0012266113080065
[10] Ptashnyk B.Yo., Il’kiv V.S., Kmit’ I.Ya., Polishchuk V.M. Nonlocal boundary value problems for partial differential equations. Naukova Dumka, Kyiv, 2002. (in Ukrainian)
[11] Savka I.Ya. Nonlocal boundary value problem for partial differential equations, constant coefficients of which lie on smooth curves. Math. Methodi Fiz.-Mekh. Polya 2009, 52 (4), 18-33. (in Ukrainian) · Zbl 1240.35097
[12] Savka I.Ya. Nonlocal problem with dependent coefficients in conditions for the second-order equation in time variable. Carpathian Math. Publ. 2010, 2 (2), 101-110. (in Ukrainian) · Zbl 1391.35110
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