Advances in Differential Equations

Bifurcation results for quasilinear elliptic systems

N. M. Stavrakakis and N. B. Zographopoulos

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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

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

First available in Project Euclid: 19 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J55
Secondary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35J60: Nonlinear elliptic equations 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]


Stavrakakis, N. M.; Zographopoulos, N. B. Bifurcation results for quasilinear elliptic systems. Adv. Differential Equations 8 (2003), no. 3, 315--336.

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