Date of Award
Master of Science
Department of Mathematics and Statistics
Aihua W. Wood, PhD
We consider the semilinear elliptic equation Δu = p(x)f(u) on a domain Ω ⊆ Rn, n ≥ 3, where f is a nonnegative function which vanishes at the origin and satisfies g1 ≤ f ≤ g2 where g1; g2 are nonnegative, nondecreasing functions which also vanish at the origin, and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary. For Ω bounded, we show that a nonnegative solution u satisfying u(x) → ∞ as x → ∂Ω exists provided the function 𝜓(s) ≡ ⌠s0 f(t) dt satisfies ⌠∞1 [𝜓(s)]-1/2 ds < ∞ For Ω unbounded (including Ω = Rn), we show that a similar result holds where u(x) → ∞ as |x| → ∞ within Ω and u(x) → ∞ as x → ∂Ω if p(x) decays to zero rapidly as |x| → ∞.
DTIC Accession Number
Proano, Zachary H., "Existence of Explosive Solutions to Non-Monotone Semilinear Elliptic Equations" (2006). Theses and Dissertations. 3348.