On the existence of periodic solutions of a semilinear wave equation with a superlinear forcing term

DOI10.21136/cmj.1988.102202zbMath0665.35050OpenAlexW2598999868MaRDI QIDQ3816437

Eduard Feireisl

Publication date: 1988

Full work available at URL: https://eudml.org/doc/13683

zbMATH Keywords

monotonicitysemilinear wave equationperiodic solutionsgrowth condition

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order nonlinear hyperbolic equations (35L70)

Related Items (12)

Periodic solutions of the wave equation with nonconstant coefficients and with homogeneous Dirichlet and Neumann boundary conditions ⋮ Periodic solutions to the wave equation with homogeneous boundary conditions ⋮ Periodic solutions of a quasilinear wave equation with homogeneous boundary conditions ⋮ On solvability of a periodic problem for a nonlinear telegraph equation ⋮ Periodic solutions of the quasilinear equation of forced vibrations of an inhomogeneous string ⋮ Nonlinear equations satisfying the nonresonance condition ⋮ Problem on periodic vibrations of an I-beam with clamped endpoint in the resonance case ⋮ On time-periodic solutions of a quasilinear wave equation ⋮ Periodic solutions to quasilinear oscillation equations for cables and beams ⋮ Time-periodic problem for a weakly nonlinear telegraph equation with directional derivative in the boundary condition ⋮ Time periodic solutions to a nonlinear wave equation with \(x\)-dependent coefficients ⋮ Periodic solutions of a quasilinear wave equation

Cites Work

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• Infinitely many periodic solutions for the equation: \(u_{tt}-u_{xx}\pm | u| ^{s-1}\,u=f(x,t)\)
• Forced vibrations of superquadratic Hamiltonian systems
• Large amplitude time periodic solutions of a semilinear wave equation
• Periodic solutions of a nonlinear wave equation

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