Electron. J. Diff. Eqns., Vol. 2006(2006), No. 29, pp. 1-16.

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

Mohammed Al-Refai, Nikos I. Kavallaris

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.

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Mohammed Al-Refai
Department of Mathematics and Statistics
Jordan University of Science and Technology
P.O. Box 3030, Ibrid 22110, Jordan
email: m_alrefai@yahoo.com
Nikos I. Kavallaris
Department of Mathematics
School of Applied Mathematical and Physical Sciences
National Technical University of Athens
Zografou Campus, 157 80 Athens, Greece
email: nkaval@math.ntua.gr

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