Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 29, pp. 1-16.

Title: Bounds and critical parameters for a class of
       non-local problems
       
Authors: Mohammed Al-Refai (Jordan Univ. of Science and Tech., Jordan)
         Nikos I. Kavallaris (National Tech. Univ. of Athens, Greece)

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.
 
Submitted November 10, 2005. Published March 16, 2006.
Math Subject Classifications: 35J65, 35B05, 35Q72.
Key Words: Non-local elliptic problems; comparison techniques.