Document Zbl 0489.35061

Periodic solutions of a nonlinear wave equation without assumption of monotonicity. (English) Zbl 0489.35061

Math. Ann. 262, 273-285 (1983).

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MSC:

35P10	Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35L70	Second-order nonlinear hyperbolic equations
35L20	Initial-boundary value problems for second-order hyperbolic equations

Keywords:

nonlinear wave equation without monotonicity; boundary and periodicity conditions; stable subspace

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References:

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[2]	Brézis, H.: Periodic solutions of nonlinear vibrating strings and duality principles. Proceedings AMS Symposium on the Mathematical Heritage of H. Poincaré. Bloomington, April 1980 · Zbl 0515.35060
[3]	Brézis, H., Coron, J.M.: Periodic solutions of nonlinear wave equations and Hamiltonian systems. Am. J. Math.103, 559-570 (1981) · Zbl 0462.35004 · doi:10.2307/2374104
[4]	Brézis, H., Coron, J.M., Nirenberg, L.: Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz. Comm. Pure Appl. Math.33, 667-689 (1980) · Zbl 0484.35057 · doi:10.1002/cpa.3160330507
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[9]	Hofer, H.: On the range of wave operator with nonmonotone nonlinearity. Math. Nachr.106, 327-340 (1982) · Zbl 0505.35058 · doi:10.1002/mana.19821060128
[10]	Marlin, J.A.: Periodic motions of coupled simple pendulums with periodic disturbances. Int. J. Nonlinear Mech.3, 439-447 (1968) · Zbl 0169.55605 · doi:10.1016/0020-7462(68)90030-9
[11]	Mawhin, J.: Une généralisation du théoréme de J.A. Marlin. Int. J. Nonlinear Mech.5, 335-339 (1970) · Zbl 0202.09501 · doi:10.1016/0020-7462(70)90030-2
[12]	Rabinowitz, P.H.: Free vibrations for a semilinear wave equation. Comm. Pure Appl. Math.31, 31-68 (1968) · Zbl 0341.35051 · doi:10.1002/cpa.3160310103
[13]	Rabinowitz, P.H.: Periodic solutions of large norm of Hamiltonian systems (to appear) · Zbl 0528.58028
[14]	Willem, M.: Densité de l’image de la différence de deux opérateurs. C.R. Acad. Sci. Paris290, 881-883 (1980) · Zbl 0436.47051
[15]	Stedry, M., Vejvoda, O.: Existence of classical periodic solutions of a wave equation: a connection of number-theoretical character of the period with geometrical properties of solutions. Differential Equations (1983) (to appear) (in Russian) · Zbl 0524.76101
[16]	Vejvoda, O.: Partial differential equations. Noordhoff: Sijthoff 1981

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