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Polynomial Harmonic Decompositions

Description: Article on polynomial harmonic decompositions. For real polynomials in two indeterminates a classical polynomial harmonic decomposition is extended from square-norm divisors to conic ones.
Date: January 2017
Creator: Anghel, Nicolae
Partner: UNT College of Arts and Sciences
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Existence and Nonexistence of Solutions for Semilinear Equations on Exterior Domains

Description: This article studies radial solutions of Δu + K(r)ƒ(u) = 0 on the exterior of the ball of radius R > 0 centered at the origin in ℝᴺ where ƒ is odd with ƒ < 0 on (0,ß), ƒ > 0 on (β, δ), ƒ ≡ 0 for u > δ, and where the function K(r) is assumed to be positive and K(r) → 0 as r → ∞.
Date: August 22, 2016
Creator: Iaia, Joseph A.
Partner: UNT College of Arts and Sciences
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Existence of Solutions for Semilinear Problems With Prescribed Number of Zeros on Exterior Domains

Description: This article proves the existence of an infinite number of radial solutions of Δ(u) + f(u) = 0 with prescribed number of zeros on the exterior of the ball of radius R > 0 centered at the origin in ℝᴺ where f is odd with f < 0 on (0, β), f > 0 on (β,∞) where β > 0.
Date: May 3, 2016
Creator: Joshi, Janak & Iaia, Joseph A.
Partner: UNT College of Arts and Sciences
open access

Existence of Solutions for Sublinear Equations on Exterior Domains

Description: This article proves the existence of an infinite number of radial solutions of Δu+K(r)ƒ(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, Bʀ, centered at the origin in ℝᴺ with u = 0 on ∂Bʀ and limᵣ→∞u(r) = 0 where N > 2, f is odd with ƒ < 0 on (0; β), ƒ > 0 on (β;∞), ƒ(u) ~ uᵖ with 0 < p < 1 for large u and K(r) ~ r-α with 0 < α < 2 for large r.
Date: October 10, 2017
Creator: Iaia, Joseph A.
Partner: UNT College of Science
open access

The Spreading of Charged Micro-Droplets

Description: This article considers the analysis of the Betelu-Fontelos model of the spreading of a charged microdroplet on a at dielectric surface whose spreading is driven by surface tension and electrostatic repulsion.
Date: January 20, 2015
Creator: Iaia, Joseph A.
Partner: UNT College of Arts and Sciences
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