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| Flat Solutions of Some Non-Lipschitz Autonomous Semilinear Equations May be Stable for {N}\geq 3 |
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Citation： |
Jes'us Ildefonso D'IAZ,Jes'us HERN'ANDEZ,Yavdat IL'YASOV.Flat Solutions of Some Non-Lipschitz Autonomous Semilinear Equations May be Stable for {N}\geq 3[J].Chinese Annals of Mathematics B,2017,38(1):345~378 |
| Page view： 775
Net amount： 853 |
Authors： |
Jes'us Ildefonso D'IAZ; Jes'us HERN'ANDEZ;Yavdat IL'YASOV |
Foundation： |
This work was supported by the projects of the DGISPI
(Spain) (Ref. MTM2011-26119, MTM2014-57113) and the UCM Research
Group MOMAT (Ref.910480). |
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| Abstract： |
The authors prove that flat ground state solutions (i.e. minimizing
the energy and with gradient vanishing on the boundary of the
domain) of the Dirichlet problem associated to some semilinear
autonomous elliptic equations with a strong absorption term given by
a non-Lipschitz function are unstable for dimensions ${N}=1,2$ and
they can be stable for ${N}\geq 3$ for suitable values of the
involved exponents. |
Keywords： |
Semilinear elliptic and parabolic equation, Strong absorption,Spectral problem, Nehari manifolds, Pohozaev identity, Flatsolution, Linearized stability, Lyapunov function, Globalinstability |
Classification： |
35J60, 35J96, 35R35, 53C45 |
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