Positivity for the linearized problem for semilinear equations

Philip Korman, Tiancheng Ouyang

DOI: http://dx.doi.org/10.12775/TMNA.2006.019

Abstract


Using recent results of M. Tang [< i> Uniqueness of positive radial solutions for $\Delta u − u + u^p = 0$ on an annulus< /i> ,
J. Differential Equations < b> 189< /b> (2003), no. 1, 148–160], we provide a simple approach
to proving positivity for the linearized problem of semilinear equations,
which is crucial for establishment of exact multiplicity results, and
for symmetry breaking.

Keywords


Positivity for the linearized problem; symmetry breaking

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