Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for N ≥ 3

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 ≥ 3 for suitable values of the involved exponents.

Keywords

Semilinear elliptic and parabolic equation / Strong absorption / Spectral problem / Nehari manifolds / Pohozaev identity / Flat solution / Linearized stability / Lyapunov function / Global instability

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