#### Filter Results:

- Full text PDF available (6)

#### Publication Year

1988

2006

- This year (0)
- Last 5 years (0)
- Last 10 years (0)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Alan V. Lair, Aihua Wood
- 1999

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)

It is a premise of this research that prevention of near-term terrorist attacks requires an understanding of current terrorist organizations to include their composition, the actors involved, and how they operate to achieve their objectives. To aid in this understanding, operations research, sociological, and behavioral theory relevant to the study of… (More)

- Alan V. Lair
- 2004

The author proves that the abstract differential inequality [[u’ (t) A(t)u(t),,2[[ 7 (t) + ()d in which the linear operator A(t) M(t) + 0 N(t), M symmetric and N antisymmetric, is in general unbounded, w(t) t-2(t)[[u(t)[[ 2 + [[M(t)u(t)[[ [[u(t)[[ and 7 is a positive constant has a nontrivial solution near t-0 i which vanishes at t-0 if and only if… (More)

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

We show that the reaction-diffusion system ut = ∆φ(u) + f (v), vt = ∆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 ⊆ RN (N ≥ 1) is bounded with smooth boundary.… (More)

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

ed Rules & Facts Data Mining EXPERT A n a l y s e s KE Tools ID3, HUGIN KBVM

We consider the semilinear elliptic equation 4u = p(x)uα + q(x)uβ on a domain Ω ⊆ Rn, n ≥ 3, where p and q are nonnegative continuous functions with the property that each of their zeroes is contained in a bounded domain Ωp or Ωq, respectively in Ω such that p is positive on the boundary of Ωp and q is positive on the boundary of Ωq. For Ω bounded, we show… (More)

- ‹
- 1
- ›