Advances in Differential Equations

Bifurcation results for quasilinear elliptic systems

N. M. Stavrakakis and N. B. Zographopoulos

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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.


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