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

DOI10.1017/S0013091516000092zbMath1379.35006WikidataQ104413704 ScholiaQ104413704MaRDI QIDQ2976361

Donal O'Regan, Andrzej F. Nowakowski

Publication date: 28 April 2017

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

forced vibrationsdual variational methodperiodic Navier problemsemilinear plate equation

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Plates (74K20) Variational methods applied to PDEs (35A15) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Higher-order semilinear hyperbolic equations (35L76)

Cites Work

• Finite time blow-up and global solutions for fourth order damped wave equations
• Bifurcation theory. An introduction with applications to partial differential equations
• Periodic solutions of some semilinear wave equations and systems: a survey.
• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• Diophantine approximation
• Periodic solutions of a nonlinear wave equation without assumption of monotonicity
• The periodic-Dirichlet problem for some semilinear wave equations
• Iterative and variational methods for the solvability of some semilinear equations in Hilbert spaces
• Periodic solutions of a wave equation with concave and convex nonlinearities
• Periodic solutions of nonlinear wave equations with general nonlinearities
• Multiplicity of periodic solutions of nonlinear wave equations.
• Nonlinear standing and rotating waves on the sphere
• Families of periodic orbits for some PDE's in higher dimensions.
• Construction of periodic solutions of nonlinear wave equations in higher dimension
• Forced vibrations of wave equations with non-monotone nonlinearities
• On the existence of periodic solutions for the equations \(D_{tt}u + (-1)^{p} D_{x}^{2p} u = \varepsilon f(\cdot,\cdot,u)\)
• Periodic solutions of nonlinear vibrating strings and duality principles
• Newton's method and periodic solutions of nonlinear wave equations
• Free nonlinear vibrations for plate equations on the equilateral triangle
• Families of periodic solutions of resonant PDEs

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