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On the Henon-Lane-Emden conjecture
Liouville-type theorems Non-linear elliptic systems Finite Morse index solutions Henon-Lane-Emden conjecture
2011/9/22
Abstract: We consider the problem of non-existence of solutions for the following H\'{e}non-Lane-Emden system {eqnarray*}
\{{array}{lcl} \hfill -\Delta u&=& |x|^{a}v^p \ \ \text{in} \mathbb{R}^N, \h...
The Glassey conjecture with radially symmetric data
Glassey conjecture semilinear wave equations Morawetz estimates KSS estimates
2011/8/25
Abstract: In this paper, we verify the Glassey conjecture in the radial case for all spatial dimensions, which states that, for the nonlinear wave equations of the form $\Box u=|\nabla u|^p$, the crit...
The Entropy Conjecture for Diffeomorphisms away from Tangencies
Entropy conjecture principal symbolic extensions
2011/1/17
We prove that every C1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant.Consequently, such diffeomorphisms satisfy Shub’s entropy conjectu...