### Positivity for the linearized problem for semilinear equations

#### 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.

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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