Date of Award

3-2006

Document Type

Thesis

Degree Name

Master of Science

Department

Department of Mathematics and Statistics

First Advisor

Aihua W. Wood, PhD

Abstract

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| → ∞.

AFIT Designator

AFIT-GAM-ENC-06-03

DTIC Accession Number

ADA446264

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