Multiplicity of solutions of the Dirichlet problem for an equation with the $p$-Laplacian in a three-dimensional spherical layer
Sergey Kolonitskii · St Petersburg Mathematical Journal · 2011
The equation $-\Delta _p u = u^{q-1}$ with zero Dirichlet condition on the boundary is considered in a three-dimensional spherical layer. The existence of arbitrarily many distinct positive solutions in a sufficiently thin layer is proved.