Slowly decaying radial solutions of an elliptic equation with subcritical and supercritical exponents (Q327611)

The authors study radial solutions of the problem \[ \Delta u + u^p + u^q=0,\quad u>0\text{ in } \mathbb R^N,\;N \geq 3 \] and \({{N}\over{N-2}}<p< {{N+2}\over{N-2}}<q.\) It is proved that if \(p\) is close to \(N/(N-2),\) \(q\) is close to \((N+2)/(N-2),\) and a certain relation holds between them, then the problem has slowly decaying solutions.