Mohammed Al-Refai, Nikos I. Kavallaris
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.
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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 |
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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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