## Abstract

The existence of at least one classical T-periodic solution is proved for di erential equations of the form (φ(u'))' - g(x, u) = h(x) when φ : (-a, a) → R is an increasing homeomorphism, g is a Carathéodory function T-periodic with respect to x, 2π-periodic with respect to u, of mean value zero with respect to u, and h ∈ L^{1} _{loc}(R) is T- periodic and has mean value zero. The problem is reduced to finding a minimum for the corresponding action integral over a closed convex subset of the space of T-periodic Lipschitz functions, and then to show, using variational inequalities techniques, that such a minimum solves the di erential equation. A special case is the relativistic forced pendulum equation" {equation presented}.

Original language | English (US) |
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Pages (from-to) | 801-810 |

Number of pages | 10 |

Journal | Differential and Integral Equations |

Volume | 23 |

Issue number | 9-10 |

State | Published - Sep 1 2010 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics