Periodic solutions of the equation \(u_{tt}-u_{xx}+u^ 3=0\)

DOI10.1007/BF01077432zbMath0837.35012MaRDI QIDQ1813186

E. I. Shul'man, B. V. Lidskij

Publication date: 25 June 1992

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

periodic solutions with small amplitude

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Second-order nonlinear hyperbolic equations (35L70)

Related Items (16)

Aspects of PDEs Related to Fluid Flows ⋮ A KAM theorem with applications to partial differential equations of higher dimensions ⋮ Quasi-periodic solutions of completely resonant nonlinear wave equations ⋮ Quasi-periodic solutions of completely resonant wave equations with quasi-periodically forced vibrations ⋮ Multiplicity and regularity of large periodic solutions with rational frequency for a class of semilinear monotone wave equations ⋮ Quasi-periodic solutions of a non-autonomous wave equations with quasi-periodic forcing ⋮ Quasi-periodic solutions for 1D wave equation with higher order nonlinearity ⋮ Quasiperiodic solutions of completely resonant wave equations with quasiperiodic forced terms ⋮ Cantor families of periodic solutions for completely resonant wave equations ⋮ Periodic solutions for the Schrödinger equation with nonlocal smoothing nonlinearities in higher dimension ⋮ Quasi-periodic solutions for 1D wave equation with the nonlinearity \(u2p+1\) ⋮ Periodic solutions for forced vibrations of wave equation with general nonlinearities: the multidimensional case ⋮ Periodic solutions for completely resonant nonlinear wave equations with Dirichlet boundary conditions ⋮ Forced vibrations via Nash-Moser iteration ⋮ A property of exponential stability in nonlinear wave equations near the fundamental linear mode ⋮ Quasi-periodic solutions of nonlinear wave equations with quasi-periodic forcing

Cites Work

• An invariant measure for the equation \(u_{tt}-u_{xx}+u^ 3=0\)

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