کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417746 | 1339305 | 2015 | 32 صفحه PDF | دانلود رایگان |
We consider the elliptic equation Îu+K(|x|)eu=0 in Rn\{0} with n>2 when for â>â2, K(r) behaves like râ near 0 or â. The asymptotic behavior of radial solutions at â is described by â(2+â)logâ¡r for â>â2 and âlogâ¡logâ¡r for â=â2. When rââK(r)âc>0 as rââ and râ0, regular radial solutions at â and singular radial solutions at 0 exhibit self-similarity at â and 0, respectively. Singular solutions with the asymptotic self-similarity exist uniquely in the radial class. Moreover, for nâ¥10+4â, separation of any two radial solutions with the asymptotic self-similarity may happen, while intersection of two solutions may occur for 20, then any two radial solutions do not intersect each other and each radial solution is linearly stable. When nâ¥10+4â, we apply the global results to prove the uniqueness of positive radial solutions for the Dirichlet problem with zero data on a ball.
Journal: Journal of Mathematical Analysis and Applications - Volume 428, Issue 2, 15 August 2015, Pages 1085-1116