## Differential and Integral Equations

- Differential Integral Equations
- Volume 17, Number 7-8 (2004), 835-848.

### The sign-changing solutions for singular critical growth semilinear elliptic equations with a weight

#### Abstract

By means of variational method, we study a singular critical growth semilinear elliptic problem: $-\Delta{u}=Q(x)|u|^{2^*-2}{u}+\mu \frac{u}{|x|^2}+\lambda u,$ $u\in H^1_0(\Omega)$, where $2^*=\frac{2N}{N-2},$ $N\geq 7,$ $0 <\mu <\frac{(N-2)^2}{4},$ $\lambda>0$, and $Q(x)$ is a positive function on $\overline{\Omega}$. By investigating the effect of the coefficient of the critical nonlinearity, we prove the existence of sign-changing solutions.

#### Article information

**Source**

Differential Integral Equations, Volume 17, Number 7-8 (2004), 835-848.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060332

**Mathematical Reviews number (MathSciNet)**

MR2075409

**Zentralblatt MATH identifier**

1150.35392

**Subjects**

Primary: 35J60: Nonlinear elliptic equations

Secondary: 35B33: Critical exponents 47J30: Variational methods [See also 58Exx]

#### Citation

Han, Pigong; Liu, Zhaoxia. The sign-changing solutions for singular critical growth semilinear elliptic equations with a weight. Differential Integral Equations 17 (2004), no. 7-8, 835--848. https://projecteuclid.org/euclid.die/1356060332