### Symmetry results for perturbed problems and related questions

DOI: http://dx.doi.org/10.12775/TMNA.2003.013

#### Abstract

In this paper we prove a symmetry result for positive solutions of the Dirichlet problem

$$

\cases

-\Delta u=f(u) & \hbox{in }D,\\

u=0 & \hbox{on }\partial D,

\endcases

\tag{0.1}

$$

when $f$ satisfies suitable assumptions and $D$ is a small symmetric perturbation of a domain $\Omega$

for which the Gidas-Ni-Nirenberg symmetry theorem applies.

We consider both the case when $f$ has subcritical growth and $f(s)=s^{(N+2)/(N-2)}+\lambda s$,

$N\ge3$, $\lambda$ suitable positive constant.

$$

\cases

-\Delta u=f(u) & \hbox{in }D,\\

u=0 & \hbox{on }\partial D,

\endcases

\tag{0.1}

$$

when $f$ satisfies suitable assumptions and $D$ is a small symmetric perturbation of a domain $\Omega$

for which the Gidas-Ni-Nirenberg symmetry theorem applies.

We consider both the case when $f$ has subcritical growth and $f(s)=s^{(N+2)/(N-2)}+\lambda s$,

$N\ge3$, $\lambda$ suitable positive constant.

#### Keywords

Elliptic equations; symmetry of solutions

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.