Cantor families of periodic solutions for completely
resonant wave equations

doi:10.1007/s11464-008-0011-3

Front. Math. China

2008, Vol. 3

Issue (2) : 151-165 https://doi.org/10.1007/s11464-008-0011-3

Cantor families of periodic solutions for completely resonant wave equations

BERTI Massimiliano¹, BOLLE Philippe²

1.Dipartimento di Matematica e Applicazioni R. Caccioppoli, Universite Federico II di Napoli, Via Cintia; 2.Laboratoire d'Analyse non lineaire et Geometrie, Universite d'Avignon;

Download: PDF(189 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods.

Issue Date: 05 June 2008

Cite this article:

BERTI Massimiliano,BOLLE Philippe. Cantor families of periodic solutions for completely resonant wave equations[J]. Front. Math. China, 2008, 3(2): 151-165.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-008-0011-3
https://academic.hep.com.cn/fmc/EN/Y2008/V3/I2/151

1	Ambrosetti A Rabinowitz P Dual variational methods incritical point theory and applicationsJFunc Anal 1973 14349381. doi:10.1016/0022‐1236(73)90051‐7
2	Baldi P Berti M Periodic solutions of waveequations for asymptotically full measure sets of frequenciesRend Mat Acc Naz Lincei 2006 17257277
3	Bambusi D Paleari S Families of periodic solutionsof resonant PDEsJ Nonlinear Sci 2001 116987. doi:10.1007/s003320010010
4	Berti M Bolle P Periodic solutions of nonlinearwave equations with general nonlinearitiesComm Math Phys 2003 243315328. doi:10.1007/s00220‐003‐0972‐8
5	Berti M Bolle P Multiplicity of periodic solutionsof nonlinear wave equationsNonlinear Anal 2004 5610111046. doi:10.1016/j.na.2003.11.001
6	Berti M Bolle P Cantor families of periodicsolutions for completely resonant nonlinear wave equationsDuke Math J 2006 134359419. doi:10.1215/S0012‐7094‐06‐13424‐5
7	Berti M Bolle P Cantor families of periodicsolutions for wave equations via a variational principleAdvances in Mathematics 2008 21716711727. doi:10.1016/j.aim.2007.11.004
8	Berti M Bolle P Cantor families of periodicsolutions of wave equations with C^k nonlinearitiesNonlinear Differential Equations and Applications(in press)
9	Bourgain J Periodicsolutions of nonlinear wave equationsIn: Harmonic Analysis and Partial Differential Equations. Chicago Lecturesin MathChicagoUniv Chicago Press 1999 6997
10	Craig W Wayne E Newton's method and periodicsolutions of nonlinear wave equationCommPure Appl Math 1993 4614091498. doi:10.1002/cpa.3160461102
11	Fadell E R Rabinowitz P Generalized cohomological indextheories for Lie group actions with an application to bifurcationquestions for Hamiltonian systemsInv Math 1978 45139174. doi:10.1007/BF01390270
12	Gentile G Mastropietro V Procesi M Periodic solutions for completely resonant nonlinear waveequationsComm Math Phys 2005 256437490. doi:10.1007/s00220‐004‐1255‐8
13	Lidskij B V Shulman E Periodic solutions of the equation u_tt - u_xx + u³ = 0Funct Anal Appl 1988 22332333. doi:10.1007/BF01077432
14	Moser J Periodicorbits near an equilibrium and a theorem by Alan WeinsteinComm Pure Appl Math 1976 29724747. doi:10.1002/cpa.3160290613
15	Struwe M Theexistence of surfaces of constant mean curvature with free boundariesActa Math 1988 1601964. doi:10.1007/BF02392272
16	Weinstein A Normalmodes for nonlinear Hamiltonian systemsInv Math 1973 204757. doi:10.1007/BF01405263
17	Yuan X Quasi-periodicsolutions of completely resonant nonlinear wave equationsJ Diff Equations 2006 230213274. doi:10.1016/j.jde.2005.12.012

Viewed

Full text

Abstract

Cited

Shared

Discussed