The Neumann Problem for the Generalized Hénon Equation

Аннотация

We study the behavior of radial solutions to the boundary value problem

\( -{\varDelta}_pu+{u}^{p-1}={\left|x\right|}^a{u}^{q-1}\; in\;B,\kern1em \frac{\partial u}{\mathrm{\partial n}}=0\; on\;\partial B,\kern1em q>p, \)

in the unit ball B and prove the existence of nonradial positive solutions for some values of parameters. We obtain multiplicity results which are new even in the case p = 2.