Bifurcating Solutions of a Nonlinear Elliptic Neumann Problem on Large Spherical Caps

Abstract

We consider the scalar-field type nonlinear elliptic equation under the homogeneous Neumann condition on a spherical cap. We discuss all the non-trivial solutions which bifurcate from the trivial positive solution. We show that the bifurcating points of non-azimuthal solutions are close to each other when the cap covers almost whole the sphere.