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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.
open access

Loitering at the hilltop on exterior domains

Description: In this article, the author proves the existence of an infinite number of radial solutions of Δu+f(u)=0 on the exterior of the ball of radius R>0 centered at the origin and f is odd with f<0 on (0,β), f>0 on (β,δ), and f≡0 for u>δ. The primitive F(u)=∫u0f(t)dt has a "hilltop" at u=δ which allows one to use the shooting method and ODE techniques to prove the existence of solutions.
Date: November 23, 2015
Creator: Iaia, Joseph A.
open access

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.
open access

Glucose or Altered Ceramide Biosynthesis Mediate Oxygen Deprivation Sensitivity Through Novel Pathways Revealed by Transcriptome Analysis in Caenorhabditis elegans

Description: This article discusses how RNA-sequencing analysis was performed to assess how a glucose-supplemented diet and/or a hyl-2 mutation altered the transcriptome.
Date: August 5, 2016
Creator: Ladage, Mary L.; King, Skylar D.; Burks, David J.; Quan, Daniel L.; Garcia, Anastacia M.; Azad, Rajeev K. et al.
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