Solvability conditions for nonlocal problems for differential equations with operator coefficients in Dirichlet-Taylor series spaces

Il’kiv Volodymyr; Strap Nataliya

Il’kiv Volodymyr ¹ , Strap Nataliya ¹

¹ Department of Higher Mathematics, Lviv polytechnic national university, Lviv, 79007, Ukraine

Keywords: solvability conditions, Dirichlet-Taylor series spaces, differential equations

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Abstract

We establish solvability conditions of non-local boundary value problems for differential equations with the operator $B = (B_1,B_2,..., B_p),$ where $B_j ≡ z_j {\partial \over \partial z_j}, j = 1,...,p,$ in the spaces of several complex variables functions, which are Dirichlet-Taylor series with fixed spectrum. Using a metric approach we prove theorems about lower estimations of small denominators, that arising in the construction of the solutions of these problems, which indicate their unique solvability for almost all vectors composed of equations coefficients and boundary conditions parameters. Estimations of small denominators depends on the asymptotic of Dirichlet-Taylor series spectrum.

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ACS Style: Il’kiv, V.; Strap, N. Solvability conditions for nonlocal problems for differential equations with operator coefficients in Dirichlet-Taylor series spaces. Bukovinian Mathematical Journal. 2016, 1
AMA Style: Il’kiv V, Strap N. Solvability conditions for nonlocal problems for differential equations with operator coefficients in Dirichlet-Taylor series spaces. Bukovinian Mathematical Journal. 2016; 1(3-4).
Chicago/Turabian Style: Volodymyr Il’kiv, Nataliya Strap. 2016. "Solvability conditions for nonlocal problems for differential equations with operator coefficients in Dirichlet-Taylor series spaces". Bukovinian Mathematical Journal. 1 no. 3-4.

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