On bounded positive solutions of quasilinear elliptic equations in \(R^ n\) (Q913097)

If \(\phi \in C^ 0([0,\infty))\), \(\phi\geq 0\), \(\not\equiv 0\) and \(\int^{\infty}_{0}r\phi (r) dr<\infty\), then the problems \[ \nabla \cdot (\frac{\nabla u}{\sqrt{1+| \Delta u|^ 2}})=\pm \phi (| x|)u^ q,\quad q>1, \] have infinitely many bounded positive entire solutions \(u\in C^ 2({\mathbb{R}}^ n)\) (n\(\geq 3)\), \(u=u(| x|)\), each of which tends to a positive constant as \(| x| \to \infty\).