Geodesic
Bounds and critical parameters for a class of non-local problems
Electronic journal of differential equations, Tome 2006 (2006)
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.
Classification : 35J65, 35B05, 35Q72
Keywords: non-local elliptic problems, comparison techniques 
@article{EJDE_2006__2006__a74,
     author = {Al-Refai,  Mohammed and Kavallaris,  Nikos I.},
     title = {Bounds and critical parameters for a class of non-local problems},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1166.35332},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a74/}
}
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%A Kavallaris,  Nikos I.
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Al-Refai,  Mohammed; Kavallaris,  Nikos I. Bounds and critical parameters for a class of non-local problems. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a74/