Electron. J. Differential Equations, Vol. 2016 (2016), No. 304, pp. 1-12.

Boundary-value problems with integral conditions for a system of Lame equations in the space of almost periodic functions

Volodymyr S. Il'kiv, Zinovii M. Nytrebych, Petro Ya. Pukach

Abstract:
We study a problem with integral boundary conditions in the time coordinate for a system of Lame equations of dynamic elasticity theory of an arbitrary dimension. We find necessary and sufficient conditions for the existence and uniqueness of solution in the class of almost periodic functions in the spatial variables. To solve the problem of small denominators arising while constructing solutions, we use the metric approach.

Submitted July 17, 2016. Published November 28, 2016.
Math Subject Classifications: 35B30, 35L53.
Key Words: Lame equation; integral boundary conditions; small denominators.

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Volodymyr S. Il'kiv
Department of Mathematics
Lviv Polytechnic National University
12 Bandera str., Lviv 79013, Ukraine
email: ilkivv@i.ua
Zinovii M. Nytrebych
Department of Mathematics
Lviv Polytechnic National University
12 Bandera str., Lviv 79013, Ukraine
email: znytrebych@gmail.com
Petro Ya. Pukach
Department of Mathematics
Lviv Polytechnic National University
12 Bandera str., Lviv 79013, Ukraine
email: ppukach@gmail.com

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