#### Date of Award

9-2006

#### 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 Δ*u* = p(x)u^{α} + q(x)u^{β} on a domain Ω ⊆ R^{n}, n ≥ 3, where p and q are nonnegative continuous functions with the property that each of their zeroes is contained in a bounded domain Ω_{p} or Ω_{q}, respectively in Ω such that p is positive on the boundary of Ω_{p} and q is positive on the boundary of Ω_{q}. For Ω bounded, we show that there exists a nonnegative solution u such that u(x) → ∞ as x → ∂Ω if 0 < α ≤ β, β > 1, and that such a solution does not exist if 0 < α ≤ β ≤ 1. For Ω = **R**^{n}, we established conditions on p and q to guarantee the existence of a nonnegative solution u satisfying u(x) → ∞ as the |x| → ∞ for 0 < α ≤ β, β > 1, and for 0 < α is ≤ β ≤ 1. For Ω=**R**^{n} and 0 < α ≤ β < 1, we also establish conditions on *p* and *q* for the existence and nonexistence of a solution of *u* where *u* is bounded on **R**^{n}.

#### AFIT Designator

AFIT-GAM-ENC-06-05

#### DTIC Accession Number

ADA455289

#### Recommended Citation

Smith, David N., "Existence of Large Solutions to Semilinear Elliptic Equations with Multiple Terms" (2006). *Theses and Dissertations*. 3350.

https://scholar.afit.edu/etd/3350