Existence of Large Solutions to Semilinear Elliptic Equations with Multiple Terms

Author

David N. Smith

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 Δu = p(x)u^α + q(x)u^β 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 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 = Rⁿ, 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=Rⁿ 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 Rⁿ.

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