## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 39, Number 1 (2010), 67-84.

### On positive solutions for $p$-Laplacian systems with sign-changing nonlinearities

#### Abstract

We consider the existence and multiplicity of positive solutions to the quasilinear system $$ \begin{cases} -\Delta_{p_{i}}u_{i} = \mu_{i}a_{i}(x)f_{i}(u_{1},\dots,u_{n})~\text{in}~\Omega,\;i=1,\dots,n, \\[1pt] u_{i} = 0~\text{on}~\partial \Omega , \end{cases} $$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ with a smooth boundary $\partial \Omega$, $\Delta_{p_{i}}u_{i}={\rm div}(|\nabla u_{i}|^{p_{i}-2}\nabla u_{i})$, $p_{i}>1$, $\mu_{i}$ are positive parameters, and $f_{i}$ are allowed to change sign.

#### Article information

**Source**

Hokkaido Math. J., Volume 39, Number 1 (2010), 67-84.

**Dates**

First available in Project Euclid: 19 May 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1274275020

**Digital Object Identifier**

doi:10.14492/hokmj/1274275020

**Mathematical Reviews number (MathSciNet)**

MR2649327

**Zentralblatt MATH identifier**

1196.35084

**Subjects**

Primary: 35J55

Secondary: 35J60: Nonlinear elliptic equations

**Keywords**

$p$-Laplace systems sign-changing positive solutions

#### Citation

HAI, Dang Dinh. On positive solutions for $p$-Laplacian systems with sign-changing nonlinearities. Hokkaido Math. J. 39 (2010), no. 1, 67--84. doi:10.14492/hokmj/1274275020. https://projecteuclid.org/euclid.hokmj/1274275020