On global solutions of the radial \(p\)-Laplace equation. The case of large \(p\) (Q2654028)

Consider the problem \[ \frac{1}{r^{n - 1}}\frac{d}{dr}\left( {r^{n - 1}\left| {\frac{du}{dr}} \right|^{p - 2}\frac{du}{dr}} \right) = c(r,u), u(a) > 0,\quad \frac{du}{dr}\,(a) \geq 0\tag{1} \] for the radial \(p\)-Laplace operator of dimension \(n \geq 1,\) where \(p \geq n\) is a real number and \(c:[a,\infty )\times (0,\infty ) \to [0,\infty )\) is a function from the Carathéodory class \(K_{\text{loc}} ([a,\infty )\times \mathbb R)\), \(a > 1\). The obtained conditions guarantee that problem (1) has no global solutions.