In IRn (n ≥ 3), an interesting property of the semi-linear equation
Is that, when K0 is a positive constant, solutions can concentrate at any point. When K0 is not a constant, we show that concentration of solutions requires strong conditions on K0. Through the stereographic projection, the discussion can be extended to Sn, and is related to bubbling, or the blow-up phenomenon.
@article{1616,
title = {Concentration of solutions of non-linear elliptic equations involving critical Sobolev exponent},
journal = {CUBO, A Mathematical Journal},
volume = {7},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/1616}
}
Chun Leung, Man. Concentration of solutions of non-linear elliptic equations involving critical Sobolev exponent. CUBO, A Mathematical Journal, Tome 7 (2005) . http://gdmltest.u-ga.fr/item/1616/