Boundary Value Problems for the q — Laplacian on 𝕊N

Nonlinear boundary value problems for the q–Laplacian in spaces of constant positive curvature are considered. The nonlinearity is of the form of a power. Existence and nonexistence of positive radial solutions in balls is established. It turns out that the situation differs considerably from the corresponding problems in the Euclidean space. Special attention is given to the critical case which has some consequences in the calculus of variation.