## Time periodic solutions of nonlinear wave equations.(English)Zbl 0219.35062

### MSC:

 35L70 Second-order nonlinear hyperbolic equations 58J45 Hyperbolic equations on manifolds
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### References:

 [1] De Simon, L. and G. Torelli, Soluzioni periodiche di equazioni a derivate parziali di tipo iperbolico non lineari, Ren. Sem. Math. Univ. Padova 15, 380-401 (1968). · Zbl 0198.13704 [2] Hale, J. K., Periodic solutions of a class of hyperbolic equations containing a small parameter, Arch. Rat. Mech. Anal. 23, 380-398 (1967). · Zbl 0152.10002 [3] Hall, W. S., On the existence of periodic solutions for the equation Dttu+(?1)pD x 2p u=? f({$$\cdot$$},{$$\cdot$$},u), J. Diff. Eq. 7, 509-526 (1970). · Zbl 0198.14002 [4] Hall, W. S., Periodic solutions of a class of weakly nonlinear evolution equations, Arch. Rat. Mech. Anal. 39, 294-322 (1971). · Zbl 0211.12704 [5] Leray, J. and J. Schauder, Topologie et equationes functionelles, Ann. Sc. École Norm. Sup. (3) 51, 45-78 (1934). · Zbl 0009.07301 [6] Lovicarová, H., Periodic solutions of a weakly nonlinear wave equation in one dimension, Czech. Math. J. 19, 324-342 (1969). [7] Nirenberg, L., On elliptic partial diferential equations, Ann. Scuola Norm. Super. Pisa (3) 13, 1-48 (1959). [8] Nirenberg, L., Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math. 8, 648-674 (1955). · Zbl 0067.07602 [9] Rabinowitz, P. H., Periodic solutions of nonlinear hyperbolic partial differential equations, Comm. Pure Appl. Math 20, 145-205 (1967). · Zbl 0152.10003 [10] Rabinowitz, P. H. Some global results for nonlinear eigenvalue problems to appear J. Functional Anal. [11] Rabinowitz, P. H., A global theorem for nonlinear eignevalue problems and applications, to appear Proc. Sym. on Nonlinear Functional Analhysis, Madison, April 1971. [12] Torelli, G., Soluzioni periodiche dell’equtione nonlineare utt-uxx+? F(x,t,u)=0, Renad. Ist. di Matem. Univ. Trieste1, 123-137 (1969). · Zbl 0186.42903 [13] Vejvoda, O., Periodic solutions of nonlinear partial differential equations of evolution, Proc. Symposium on Diff. Eq. and Applications at Bratislava in September 1966, 293-300 (1969). · Zbl 0183.10401
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