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arXiv · 2604.26286

The Neumann problem for the generalized H\'enon equation. Local analysis

Alexander I. Nazarov·Alexandra P. Shcheglova
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Abstract

For the boundary value problem $$\left\{ \begin{array}{rcll} -\Delta_p u+u^{p-1}&=&|x|^{\alpha}u^{q-1}&\mbox{in }\Omega,\\ \frac{\displaystyle\partial u}{\displaystyle\partial{\bf n}}&=&0&\mbox{on }\partial \Omega, \end{array}\right. $$ in the unit ball $\Omega$, 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 $p$.

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Alexander I. Nazarov, Alexandra P. Shcheglova. 2026-04-29. The Neumann problem for the generalized H\'enon equation. Local analysis. https://arxiv.org/abs/2604.26286

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