Quasi-periodic solutions of completely resonant wave equations with quasi-periodically forced vibrations

DOI10.1007/S10440-010-9574-6zbMath1207.35031OpenAlexW1970508272MaRDI QIDQ607699

Yansheng Ma, Wenqi Lou

Publication date: 3 December 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-010-9574-6

zbMATH Keywords

Lyapunov-Schmidt reductionsmall divisorslinking theoremspatial periodic boundary conditions

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Almost and pseudo-almost periodic solutions to PDEs (35B15) Second-order semilinear hyperbolic equations (35L71)

Related Items (1)

Quasiperiodic solutions of completely resonant wave equations with quasiperiodic forced terms

Cites Work

• Quasi-periodic solutions of the equation \(v_{tt} - v_{xx} +v^3 = f(v)\)
• Diophantine approximation
• Periodic solutions of nonlinear wave equations with general nonlinearities
• Multiplicity of periodic solutions of nonlinear wave equations.
• Periodic solutions of the equation \(u_{tt}-u_{xx}+u^ 3=0\)
• Cantor families of periodic solutions for completely resonant nonlinear wave equations
• Time periodic solutions of nonlinear wave equations
• Quasi-periodic solutions for completely resonant nonlinear wave equations in 1D and 2D
• A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
• Newton's method and periodic solutions of nonlinear wave equations
• Quasi-Periodic Solutions of Completely Resonant Forced Wave Equations
• Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations

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