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Volume 23, Issue 3
On the Non-trivial Solvability of Boundary Value Problems in the Angle Domains

V. P. Burskii & Ye. V. Kirichenko

DOI: 10.4208/jpde.v23.n3.3

J. Part. Diff. Eq., 23 (2010), pp. 235-250.

Published online: 2010-08

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  • Abstract

In the first part of the present paper we deal with the first boundary value problem for general second-order differential equation in plane angle. The criterion of non-trivial solvability is obtained for such problem in space C^2 of functions having polynomial growth at infinity. In the second part so-called "almost Cauchy" problem in a polygon for high order differential equation without respect of type is investigated. The necessary condition of uniqueness violation of solution is appeared to be sufficient in case of problem with one boundary condition.

  • Keywords

Dirichlet problem almost Cauchy problem Fourier transform duality method equation-domain tubular domain conjugate cone

  • AMS Subject Headings

35G15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-23-235, author = {V. P. Burskii and Ye. V. Kirichenko }, title = {On the Non-trivial Solvability of Boundary Value Problems in the Angle Domains}, journal = {Journal of Partial Differential Equations}, year = {2010}, volume = {23}, number = {3}, pages = {235--250}, abstract = {

In the first part of the present paper we deal with the first boundary value problem for general second-order differential equation in plane angle. The criterion of non-trivial solvability is obtained for such problem in space C^2 of functions having polynomial growth at infinity. In the second part so-called "almost Cauchy" problem in a polygon for high order differential equation without respect of type is investigated. The necessary condition of uniqueness violation of solution is appeared to be sufficient in case of problem with one boundary condition.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v23.n3.3}, url = {http://global-sci.org/intro/article_detail/jpde/5232.html} }
TY - JOUR T1 - On the Non-trivial Solvability of Boundary Value Problems in the Angle Domains AU - V. P. Burskii & Ye. V. Kirichenko JO - Journal of Partial Differential Equations VL - 3 SP - 235 EP - 250 PY - 2010 DA - 2010/08 SN - 23 DO - http://doi.org/10.4208/jpde.v23.n3.3 UR - https://global-sci.org/intro/article_detail/jpde/5232.html KW - Dirichlet problem KW - almost Cauchy problem KW - Fourier transform KW - duality method equation-domain KW - tubular domain KW - conjugate cone AB -

In the first part of the present paper we deal with the first boundary value problem for general second-order differential equation in plane angle. The criterion of non-trivial solvability is obtained for such problem in space C^2 of functions having polynomial growth at infinity. In the second part so-called "almost Cauchy" problem in a polygon for high order differential equation without respect of type is investigated. The necessary condition of uniqueness violation of solution is appeared to be sufficient in case of problem with one boundary condition.

V. P. Burskii and Ye. V. Kirichenko . (2010). On the Non-trivial Solvability of Boundary Value Problems in the Angle Domains. Journal of Partial Differential Equations. 23 (3). 235-250. doi:10.4208/jpde.v23.n3.3
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