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


35L70 Second-order nonlinear hyperbolic equations
58J45 Hyperbolic equations on manifolds
Full Text: DOI EuDML


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.