## Advances in Differential Equations

- Adv. Differential Equations
- Volume 8, Number 3 (2003), 315-336.

### Bifurcation results for quasilinear elliptic systems

N. M. Stavrakakis and N. B. Zographopoulos

#### Abstract

We prove certain bifurcation results for the quasilinear elliptic system \begin{align*} & -\Delta_{p}u = \lambda\, a(x)\, |u|^{p-2}u+\lambda\, b(x)\, |u|^{\alpha}\, |v|^{\beta}\, v +f(x,\lambda,u,v), \\ & -\Delta_{q}v = \lambda\, d(x)\, |v|^{q-2}v+\lambda\, b(x)\, |u|^{\alpha}\, |v|^{\beta}\, u +g(x,\lambda,u,v), \end{align*} defined on an arbitrary domain (bounded or unbounded) of $\mathbb{R}^N$, where the functions $a$, $d$, $f$ and $g$ may change sign. To this end we establish the isolation of the principal eigenvalue of the corresponding unperturbed system and apply topological degree theory.

#### Article information

**Source**

Adv. Differential Equations, Volume 8, Number 3 (2003), 315-336.

**Dates**

First available in Project Euclid: 19 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1355926856

**Mathematical Reviews number (MathSciNet)**

MR1948048

**Zentralblatt MATH identifier**

1229.35068

**Subjects**

Primary: 35J55

Secondary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35J60: Nonlinear elliptic equations 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]

#### Citation

Stavrakakis, N. M.; Zographopoulos, N. B. Bifurcation results for quasilinear elliptic systems. Adv. Differential Equations 8 (2003), no. 3, 315--336. https://projecteuclid.org/euclid.ade/1355926856