On computation of bounds of the bifurcation parameter for a non-local elliptic equation with increasing nonlinearity

A novel approach is developed to prove the existence of δ∗δ∗, the supremum of the spectrum of a non-local elliptic problem associated with homogeneous Robin and Dirichlet boundary conditions. Analytical upper and lower bounds of δ∗δ∗ are obtained in closed form. The bounds are presented for the slab, cylindrical and spherical geometries.