### Citations

27 |
Sur les trajectoires du gradient d’une fonction analytique,
- Lojasiewicz
- 1983
(Show Context)
Citation Context ...(2) hal-00391964, version 1 - 5 Jun 2009 for which decay estimates have been obtained recently by Chergui [3] and Ben HassenChergui [2] when F satisfies a uniform Lojasiewicz gradient inequality (cf. =-=[9]-=- and also [7,8] for related works). Their estimates are optimal for general functions F but in the case of (1) or more generally for equations having a similar structure better results can be proved. ... |

18 |
A.: Convergence of solutions of second-order gradient-like systems with analytic nonlinearities
- Haraux, Jendoubi
- 1998
(Show Context)
Citation Context ...964, version 1 - 5 Jun 2009 for which decay estimates have been obtained recently by Chergui [3] and Ben HassenChergui [2] when F satisfies a uniform Lojasiewicz gradient inequality (cf. [9] and also =-=[7,8]-=- for related works). Their estimates are optimal for general functions F but in the case of (1) or more generally for equations having a similar structure better results can be proved. When f = 0, (1)... |

15 |
Decay estimates to equilibrium for some evolution equations with an analytic nonlinearity, Asympt
- Haraux, Jendoubi
(Show Context)
Citation Context ...964, version 1 - 5 Jun 2009 for which decay estimates have been obtained recently by Chergui [3] and Ben HassenChergui [2] when F satisfies a uniform Lojasiewicz gradient inequality (cf. [9] and also =-=[7,8]-=- for related works). Their estimates are optimal for general functions F but in the case of (1) or more generally for equations having a similar structure better results can be proved. When f = 0, (1)... |

8 |
Oscillatory blow-up in nonlinear second order ODE’s: the critical case. Discrete Contin
- Balabane, Jazar, et al.
(Show Context)
Citation Context ...ow large β can be) seems overwhelmingly small. In fact there are previous parallel results for the backward equation of (4) showing oscillatory blow up properties by a completely different method, cf =-=[1, 10]-=-. The plan of the paper is the following: Section 1 contains basic energy estimates of solutions to (4). Section 2 is devoted to the oscillatory (or non-oscillatory ) behavior of these solutions, in p... |

7 |
Critical exponents, special large-time behavior and oscillatory blow-up in nonlinear ode’s.
- Souplet
- 1998
(Show Context)
Citation Context ...ow large β can be) seems overwhelmingly small. In fact there are previous parallel results for the backward equation of (4) showing oscillatory blow up properties by a completely different method, cf =-=[1, 10]-=-. The plan of the paper is the following: Section 1 contains basic energy estimates of solutions to (4). Section 2 is devoted to the oscillatory (or non-oscillatory ) behavior of these solutions, in p... |

6 |
Slow and fast decay of solutions to some second order evolution equations
- Haraux
(Show Context)
Citation Context ...2 , then for each solution u of (4) which satisfies (3.1) there is a constant C such that ∀t ≥ 1, 1−α − |u(t)| ≤ Ct α and ∀t ≥ 1, |u ′ 1 − (t)| ≤ Ct α Remark 3.3. Theorem 3.1 generalizes Theorem 1 of =-=[6]-=- corresponding to the case α = 0, in which there are exceptional solutions which decay at the maximal rate permitted by the lower bound of the energy decay, which is in that case exponential. 14Such ... |

4 |
Convergence of global and bounded solutions of a second order gradient like system with nonlinear dissipation and analytic nonlinearity
- Chergui
(Show Context)
Citation Context ...uation is a special case of the vector evolution problem u ′′ + c‖u ′ ‖ α u ′ + ∇F (u) = f(t) (2) hal-00391964, version 1 - 5 Jun 2009 for which decay estimates have been obtained recently by Chergui =-=[3]-=- and Ben HassenChergui [2] when F satisfies a uniform Lojasiewicz gradient inequality (cf. [9] and also [7,8] for related works). Their estimates are optimal for general functions F but in the case of... |

3 |
Asymptotics for some nonlinear O.D.E of the second order, Nonlinear Analysis 10
- Haraux
- 1986
(Show Context)
Citation Context ...ot identically 0 changes sign on each interval (T, ∞) and so does u ′ (t). Proof. As a consequence of the lifting theorem, since the energy of u is positive for all t we can introduce, as was done in =-=[5]-=-, polar coordinates as follows 2 ( β + 2 ) 1 2 |u| β 2 u = r(t) cos θ(t), u ′ (t) = r(t) sin θ(t) (2.3) 7where r and θ are two C 1 functions and r(t) = E(t) 1 2 > 0. A straighforward calculation show... |

2 |
On the asymptotic behavior of solutions of a damped oscillator under a sublinear friction term: from the exceptional to the generic behaviors
- Diaz, Linan
- 2002
(Show Context)
Citation Context ... there are exceptional solutions which decay at the maximal rate permitted by the lower bound of the energy decay, which is in that case exponential. 14Such a result is also known for α < 0, cf. eg. =-=[4]-=-. The following result shows that if 0 < α < α0 := β β+2 there are indeed non-trivial solutions of (4) which satisfy (3.1). Theorem 3.4. Let α < β β+2 , c > 0. Then there exists a solution u > 0 of (4... |

1 | version 1 - 5 - hal-00391964 - 2009 |