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Periodic Navier Solutions for the Plate Equation with Non-Monotone Nonlinearities: the Multidimensional Case

Part of: Hyperbolic equations and systems Partial differential equations

Published online by Cambridge University Press:  19 May 2016

Andrzej Nowakowski  and
Donal O'regan
Andrzej Nowakowski
Affiliation:
University of Lodz, Banacha 22, 90-238 Lodz, Poland (annowako@math.uni.lodz.pl)
Donal O'regan
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, University Road, Galway, Ireland
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Abstract

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We discuss the solvability of the periodic Navier problem for the plate equation with forced vibrations xtt (t, y)+Δ2 x(t, y)+l(t, y, x(t, y)) = 0 in higher dimensions with side lengths being irrational numbers and the nonlinearity being superlinear. We also derive a new dual variational method.

Keywords

periodic Navier problemsemilinear plate equationdual variational method

MSC classification

Secondary: 35B10: Periodic solutions 35L75: Nonlinear higher-order hyperbolic equations 35A15: Variational methods
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 1 , February 2017 , pp. 203 - 230
Copyright
Copyright © Edinburgh Mathematical Society 2016