The existence of periodic solutions of nonlinear wave equations on Sn

DOI10.1080/03605308708820511zbMath0627.35063OpenAlexW2091623962MaRDI QIDQ3762969

Zhengfang Zhou

Publication date: 1987

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308708820511

zbMATH Keywords

monotonicitygrowthexistenceapproximationcritical pointsnonlinear wave equationvariational methodPerturbationsT-periodic solutionsinfinitely many pairs of solutions

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Variational methods applied to PDEs (35A15) Second-order nonlinear hyperbolic equations (35L70) Perturbations in context of PDEs (35B20)

Related Items (4)

Multiplicity and regularity of large periodic solutions with rational frequency for a class of semilinear monotone wave equations ⋮ Sobolev Estimates for the Wave Operator on compact Manifolds ⋮ The wave operator on \(S^ n:\) Estimates and applications ⋮ Subharmonic solutions of nonlinear wave equations on \(S^n\)

Cites Work

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• The dual method in critical point theory. Multiplicity results for indefinite functional
• Critical point theorems for indefinite functionals
• Periodic solutions of a nonlinear wave equation without assumption of monotonicity
• Topological results on a certain class of functionals and application
• Periodic solutions of nonlinear vibrating strings and duality principles
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Infinitely many periodic solutions for the equation
• Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz
• Forced vibrations for a nonlinear wave equation

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