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We show that large positive solutions exist for the equation (P±) :∆u±|∇u|q = p(x)uγ in Ω ⊆ RN(N ≥ 3) for appropriate choices of γ > 1,q > 0 in which the domain Ω is either bounded or equal to RN . The nonnegative function p is continuous and may vanish on large parts of Ω. If Ω = RN , then p must satisfy a decay condition as |x| →∞. For (P+), the decay… (More)

- Jonathan T. Hamill, Richard F. Deckro Chairman, Alan V. Lair
- 2006

- Alan V. Lair
- Int. J. Math. Mathematical Sciences
- 2005

We show that the reaction-diffusion system u t = ∆ϕ(u) + f (v), v t = ∆ψ(v) + g(u), with homogeneous Neumann boundary conditions, has a positive global solution on Ω × [0,∞) if and only if ∞ ds/ f (F −1 (G(s))) = ∞ (or, equivalently, ∞ ds/g(G −1 (F(s))) = ∞), where F(s) = s 0 f (r)dr and G(s) = s 0 g(r)dr. The domain Ω ⊆ R N (N ≥ 1) is bounded with smooth… (More)

Approved for public release; distribution unlimited The views expressed in this dissertation are those of the author and do not reeect the oocial policy or position of the Department of Defense or the United States Government. Acknowledgements I must foremost thank God for his unending patience and love. It was said to me while at AFIT the Lord does not… (More)

- Timothy D. Ross, Alan V. Lair
- Pattern Recognition
- 1988

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