## Differential and Integral Equations

- Differential Integral Equations
- Volume 16, Number 7 (2003), 769-786.

### Symmetry of solutions of a semilinear elliptic equation with unbounded coefficients

#### Abstract

We study the equation $- \Delta u + |x|^a |u|^{q-2} u = |x|^b |u|^{p-2} u$ with Dirichlet boundary condition on $B(0,1)$ or on $\mathbb R^N$. We study the radial solutions of this equation on~$\mathbb R^N$ and the symmetry breaking for ground states for $q=2$ on $\mathbb R^N$. Estimates of the transition are also given when $p$ is close to $2$ or $2^*$ on $B(0,1)$.

#### Article information

**Source**

Differential Integral Equations, Volume 16, Number 7 (2003), 769-786.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060596

**Mathematical Reviews number (MathSciNet)**

MR1988724

**Zentralblatt MATH identifier**

1161.35398

**Subjects**

Primary: 35J60: Nonlinear elliptic equations

Secondary: 35A15: Variational methods 35A30: Geometric theory, characteristics, transformations [See also 58J70, 58J72] 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35J20: Variational methods for second-order elliptic equations

#### Citation

Sintzoff, Paul. Symmetry of solutions of a semilinear elliptic equation with unbounded coefficients. Differential Integral Equations 16 (2003), no. 7, 769--786. https://projecteuclid.org/euclid.die/1356060596