TY - JOUR
T1 - Bubbling solutions for an anisotropic Emden-Fowler equation
AU - Wei, Juncheng
AU - Ye, Dong
AU - Zhou, Feng
PY - 2006/8/15
Y1 - 2006/8/15
N2 - We consider the anisotropic Emden-Fowler equation: ∇ (a (x) ∇ u) + ε2 a (x) eu = 0 in Ω, u = 0 on ∂Ω where Ω ⊂ R2 is a smooth bounded domain and a (x) is a positive, smooth function. We investigate the effect of anisotropic coefficient a (x) on the existence of bubbling solutions. We show that at given strict local maximum points of a, there exist solutions with arbitrarily many bubbles. As a consequence, the quantityTε = ε2 under(∫, Ω) a (x) eu d x can approach to +∞ as ε → 0. These results show a striking difference with the isotropic case (a (x) ≡ constant). To cite this article: J. Wei et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
AB - We consider the anisotropic Emden-Fowler equation: ∇ (a (x) ∇ u) + ε2 a (x) eu = 0 in Ω, u = 0 on ∂Ω where Ω ⊂ R2 is a smooth bounded domain and a (x) is a positive, smooth function. We investigate the effect of anisotropic coefficient a (x) on the existence of bubbling solutions. We show that at given strict local maximum points of a, there exist solutions with arbitrarily many bubbles. As a consequence, the quantityTε = ε2 under(∫, Ω) a (x) eu d x can approach to +∞ as ε → 0. These results show a striking difference with the isotropic case (a (x) ≡ constant). To cite this article: J. Wei et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
UR - https://www.scopus.com/pages/publications/33746271647
U2 - 10.1016/j.crma.2006.05.017
DO - 10.1016/j.crma.2006.05.017
M3 - 文章
AN - SCOPUS:33746271647
SN - 1631-073X
VL - 343
SP - 253
EP - 258
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 4
ER -