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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 8
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Articles

Small amplitude periodic solutions for Kirchhoff equations with Neumann conditions

Zhenjie LiuSchool of Mathematics, Jilin University, Changchun, 130012Jilin, P.R. China.;Department of Mathematics, Harbin University, Harbin, 150086Heilongjiang, P.R. China.Correspondence[email protected]
Pages 1695-1708 | Received 08 Dec 2013, Accepted 09 Jun 2014, Published online: 30 Jul 2014

References

  • Kirchhoff G. Vorlesungen über mechanik [Lectures on mechanics]. Leipzig: Teubner; 1883.
  • Kirchhoff G. Vorlesungen über mathematische physik: mechanik [Lectures on mathematical physics: mechanics]. Leipzig: Teubner; 1876.
  • Bernstein S. Sur une classe d’équations fonctionnelles aux dérivées partielles [On a class of functional partial differential equations]. Izv. Akad. Nauk SSSR Ser. Mat. 1940;4:17–26.
  • D’Ancona P, Spagnolo S. Nonlinear perturbations of the Kirchhoff equation. Commun. Pure Appl. Math. 1994;47:1005–1029.
  • Ghisi M. Asymptotic behaviour for the Kirchhoff equation. Ann. Mat. Pur. Appl. 1996;171:293–312.
  • Hirosawa F. Global solvability for Kirchhoff equation in special classes of non-analytic functions. J. Differ. Equ. 2006;230:49–70.
  • Manfrin R. Global solvability to the Kirchhoff equation for a new class of initial data. Portugaliae Math. 2002;59:91–109.
  • Manfrin R. On the global solvability of Kirchhoff equation for non-analytic initial data. J. Differ. Equ. 2005;211:38–60.
  • Miranda MM, Jutuca LPSG. Existence and boundary stabilization of solutions for the Kirchhoff equation. Commun. Partial Differ. Equ. 1999;24:1759–1800.
  • Peradze J. A numerical algorithm for the nonlinear Kirchhoff string equation. Numer. Math. 2005;102:311–342.
  • Rzymowski W. One-dimensional Kirchhoff equation. Nonlinear Anal. 2002;48:209–221.
  • Yamazaki T. Global solvability for the Kirchhoff equations in exterior domains of dimension three. J. Differ. Equ. 2005;210:290–316.
  • Baldi P. Periodic solutions of forced Kirchhoff equations. Ann. Scuola Norm. Sup. Pisa-Cl. di Sci. 2009;8:117–141.
  • Baldi P, Berti M. Forced vibrations of a nonhomogeneous string. SIAM J. Math. Anal. 2008;40:382–412.
  • Baldi P, Berti M. Periodic solutions of nonlinear wave equations for asymptotically full measure sets of frequencies. Rend. Lincei Mat. Appl. 2006;17:257–277.
  • Berti M. Nonlinear oscillations of Hamiltonian PDEs. Progress in Nonlinear Differential Equations and Their Applications. Vol. 74. Boston: Birkhäuser; 2008.
  • Berti M, Bolle P. Cantor families of periodic solutions for completely resonant nonlinear wave equations. Duke Math. J. 2006;134:359–419.
  • Berti M, Bolle P. Cantor families of periodic solutions for wave equations via a variational principle. Adv. Math. 2008;217:1671–1727.
  • Berti M, Bolle P. Cantor families of periodic solutions of wave equations with {\it C}\textsuperscript{{\it k}} nonlinearities. Nonlinear Differ. Equ. Appl. 2008;15:247–276.
  • Berti M, Bolle P. Multiplicity of periodic solutions of nonlinear wave equations. Nonlinear Anal. 2004;56:1011–1046.
  • Kröger P. Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space. J. Func. Anal. 1992;106:353–357.

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