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Existence and nonexistence of radial solutions for semilinear equations with bounded nonlinearities on exterior domains
Article studies radial solutions of ∆u + K(r)f(u) = 0 on the exterior of the ball of radius R > 0 centered at the origin in ℝᶰ where f is odd with f < 0 on (0, β), f > 0 on (β, δ), f ≡ 0 for u > δ, and where the function K(r) is assumed to be positive and K(r) → 0 as r → ∞.
Date:
December 1, 2020
Creator:
Iaia, Joseph A.
System:
The UNT Digital Library
On Polish groups admitting non-essentially countable actions
Article addresses the question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. The authors e answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space.
Date:
September 17, 2019
Creator:
Kechris, Alexander S.; Malicki, Maciej; Panagiotopoulos, Aristotelis & Zielinski, Joseph
System:
The UNT Digital Library