On Some Difference Equations of First Order

Vladimir B. Vasilyev

doi:10.2478/tmmp-2013-00013

.blurhash-client-img { display: none !important; }

On Some Difference Equations of First Order

Tatra Mountains Mathematical Publications

Volume 54 (2013): Issue 1 (April 2013)

By: Vladimir B. Vasilyev

Open Access

|Jul 2013

Abstract

One considers two boundary value problems for the Laplacian and biharmonic operator in a plane sector with boundary conditions of the Dirichlet and the Neumann type on the angle sides. The system of difference equations of first order to which this problem is reduced, is explicitly written out. Certain cases of solvability for such difference equations of first order are described; it will be useful for studying similar equations.

References

[1] VASILYEV, V. B.: Elliptic equations and boundary value problems in non-smooth domains, in: Oper. Theory Adv. Appl., Vol. 213, Birkh¨auser, Basel, 2011, pp. 105-121.10.1007/978-3-0348-0049-5_6
Search in Google Scholar
[2] MILNE-THOMSON, L. M.: The Calculus of Finite Differences. Chelsea Publ. Comp., New York, 1981.
Search in Google Scholar
[3] TITCHMARSH, E.: Introduction to the Theory of Fourier Integrals. Chelsea Publ. Comp., New York, 1986.
Search in Google Scholar
[4] VASIL’EV, V. B.: Wave Factorization of Elliptic Symbols: Theory and Applications. Introductionto the theory of boundary value problems in non-smooth domains. Kluwer Acad. Publ., Dordrecht, 2000.10.1007/978-94-015-9448-6_9
Search in Google Scholar
[5] SOLONNIKOV, V. A.-FROLOVA, E. V.: On the third value problem for the Laplaceequation in a plane sector and application to parabolic problems, Algebra Anal. 2 (1990), 213-241.
Search in Google Scholar
[6] BAZALIY, B. V.-VASYLYEVA, N.: On the solvability of a transmission problem for theLaplace operator with a dynamic boundary condition on a nonregular interface, J. Math. Anal. Appl. 393 (2012), 651-670.10.1016/j.jmaa.2012.03.023
Search in Google Scholar
[7] VASILYEV, V. B.: Discrete convolutions and difference equations, in: Proc. of the 5th Internat. Conf., Morehouse College, Atlanta, GA, USA, 2007 (G. S. Ladde et al., eds.), Dynam. Systems Appl., Vol. 5, Dynamic Publishers, Atlanta, USA, 2008, pp. 474-480.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2013-00013 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

Language: English

Page range: 165 - 181

Published on: Jul 4, 2013

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

boundary value problem,

Related subjects:

© 2013 Vladimir B. Vasilyev, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 54 (2013): Issue 1 (April 2013)