Bounds and critical parameters for a class of non-local problems

Abstract

A non-local elliptic equation, for which comparison methods are applicable, associated with Robin boundary conditions is considered. Upper and lower solutions for this problem are obtained by solving algebraic equations. These upper and lower solutions are used to obtain analytical bounds for the critical (blow-up) parameter of the problem. Numerical results are presented for the slab, cylindrical and spherical geometries. The results are compared with the existing ones in the literature.