### Abstract

Existence of forced vibrations of nonlinear wave equation: (formula presented)existence of infinitely many periodic solutions is proved. This improves the results of the author [29, 30]. We use variational methods to show the existence result. Minimax arguments and energy estimates for the corresponding functional play an essential role in the proof.

Original language | English |
---|---|

Pages (from-to) | 615-645 |

Number of pages | 31 |

Journal | Transactions of the American Mathematical Society |

Volume | 307 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1988 |

Externally published | Yes |

### Fingerprint

### Keywords

- Minimax method
- Nonlinear wave equation
- Periodic solution
- Perturbation
- Variational method

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*307*(2), 615-645. https://doi.org/10.1090/S0002-9947-1988-0940220-X

**Infinitely many periodic solutions for the equation.** / Tanaka, Kazunaga; Words, Key.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 307, no. 2, pp. 615-645. https://doi.org/10.1090/S0002-9947-1988-0940220-X

}

TY - JOUR

T1 - Infinitely many periodic solutions for the equation

AU - Tanaka, Kazunaga

AU - Words, Key

PY - 1988

Y1 - 1988

N2 - Existence of forced vibrations of nonlinear wave equation: (formula presented)existence of infinitely many periodic solutions is proved. This improves the results of the author [29, 30]. We use variational methods to show the existence result. Minimax arguments and energy estimates for the corresponding functional play an essential role in the proof.

AB - Existence of forced vibrations of nonlinear wave equation: (formula presented)existence of infinitely many periodic solutions is proved. This improves the results of the author [29, 30]. We use variational methods to show the existence result. Minimax arguments and energy estimates for the corresponding functional play an essential role in the proof.

KW - Minimax method

KW - Nonlinear wave equation

KW - Periodic solution

KW - Perturbation

KW - Variational method

UR - http://www.scopus.com/inward/record.url?scp=0001471330&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001471330&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1988-0940220-X

DO - 10.1090/S0002-9947-1988-0940220-X

M3 - Article

AN - SCOPUS:0001471330

VL - 307

SP - 615

EP - 645

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -