Periodic solutions to nonlinear wave equations with \(x\)-dependent coefficients at resonance

DOI10.1216/RMJ-2018-48-4-1291zbMath1403.35022OpenAlexW2895707660MaRDI QIDQ1799896

Kai Liu, Wei Shi

Publication date: 19 October 2018

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1538272834

zbMATH Keywords

Galerkin methodunique existenceglobal inversion theorem

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Resonance in context of PDEs (35B34) Second-order semilinear hyperbolic equations (35L71) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Cites Work

• Global existence for nonlinear elastic waves in high space dimensions
• An application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations
• Resonance in nonlinear wave equations with \(x\)-dependent coefficients
• Periodic solutions of wave equations with jumping nonlinearities
• Conservative systems of semi-linear wave equations with periodic Dirichlet boundary conditions
• Global existence of solutions for a weakly coupled system of semilinear damped wave equations
• The periodic boundary value problem for semilinear elastic beam equations: the resonance case
• Nonlinear boundary value problems at resonance
• Solutions of nonlinear hyperbolic equations at resonance
• L∞-optimal control of the periodic 1-D wave equation with x-dependent coefficients
• Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities
• Periodic solutions to nonlinear one dimensional wave equation with 𝑋-dependent coefficients
• Bounded resonance problems for semilinear elliptic equations

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