The Neumann problem for the generalized Hénon equation. Local analysis
For the boundary value problem $$\left\{ \begin{array}{rcll} -Δ_p u+u^{p-1}&=&|x|^αu^{q-1}&\mbox{in }Ω,\\ \frac{\displaystyle\partial u}{\displaystyle\partial{\bf n}}&=&0&\mbox{on }\partial Ω, \end{array}\right. $$ in the unit ball $Ω$, we investigate the properties of the positive radial solution. It is known, that for $1 2$ be sufficiently close to $2$. Then for all $p p$ is sufficiently close to $p$.
math.AP↗