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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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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| → +∞.

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## Abstract In this paper, we consider the non‐linear wave equation __a__,__b__>0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on __α__, __m__, and __p__, we give precise decay rates for the solution. In particular, we show that for __m__=0, the decay is ex