## Advances in Differential Equations

### Bifurcation results for quasilinear elliptic systems

#### 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

#### 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