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.
Citation
N. M. Stavrakakis. N. B. Zographopoulos. "Bifurcation results for quasilinear elliptic systems." Adv. Differential Equations 8 (3) 315 - 336, 2003. https://doi.org/10.57262/ade/1355926856
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