We use a simple and effective Hille-type technique to establish that the n-th-dimensional elliptic equation ∆u + f (x, u) + g(|x|)x • ∇u = 0, |x| > A > 0, with n ≥ 3, has positive solutions which decay to 0 as |x| → +∞.
✦ LIBER ✦
Hille’s non-oscillation theorem and the decay of solutions to a class of semi-linear PDE’s
✍ Scribed by Octavian G. Mustafa
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 131 KB
- Volume
- 89
- Category
- Article
- ISSN
- 0003-889X
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The proofs of Theorems 2 and 3 are very laborious and must be omitted. We merely mention that the proof of Theorem 2 is based on the definition of regular mapping, while the proof of Theorem 3 is based on Lemmas 6,7,17,18,and 19.