Existence of global solutions of elliptic systems
The author deals with the existence of entire solutions of elliptic systems \[ \begin{aligned} &\text{div} (| u|^\gamma |\nabla u|^{m-2} \nabla u)- \tfrac \gamma m | u|^{\gamma-2} u|\nabla u|^m=| u|^{p-2}u,\\ &u:\mathbb{R}^n\to \mathbb{R}^d, \quad\text{with }m>1, \;\gamma\in \mathbb{R},\;p>1. \end{aligned} \tag{1} \] The author proves that, if \(\gamma\geq p-m\), then (1) admits a one-parameter family of nontrivial entire radial solutions, \(u= u(| x|)\), such that \(\lim_{| x|\to\infty}| u(| x|)|= \infty\).
scientific article; zbMATH DE number 2082171