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Ulam Stabilities for Partial Impulsive Fractional Differential Equations

Saïd Abbas, Mouffak Benchohra, Juan J. Nieto (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we investigate the existence of solutions for the initial value problems (IVP for short), for a class of implicit impulsive hyperbolic differential equations by using the lower and upper solutions method combined with Schauder’s fixed point theorem.

Ultrarigid tangents of sub-Riemannian nilpotent groups

Enrico Le Donne, Alessandro Ottazzi, Ben Warhurst (2014)

Annales de l’institut Fourier

We show that the tangent cone at the identity is not a complete quasiconformal invariant for sub-Riemannian nilpotent groups. Namely, we show that there exists a nilpotent Lie group equipped with left invariant sub-Riemannian metric that is not locally quasiconformally equivalent to its tangent cone at the identity. In particular, such spaces are not locally bi-Lipschitz homeomorphic. The result is based on the study of Carnot groups that are rigid in the sense that their only quasiconformal maps...

Uncountable γ-sets under axiom C P A c u b e g a m e

Krzysztof Ciesielski, Andrés Millán, Janusz Pawlikowski (2003)

Fundamenta Mathematicae

We formulate a Covering Property Axiom C P A c u b e g a m e , which holds in the iterated perfect set model, and show that it implies the existence of uncountable strong γ-sets in ℝ (which are strongly meager) as well as uncountable γ-sets in ℝ which are not strongly meager. These sets must be of cardinality ω₁ < , since every γ-set is universally null, while C P A c u b e g a m e implies that every universally null has cardinality less than = ω₂. We also show that C P A c u b e g a m e implies the existence of a partition of ℝ into ω₁ null compact sets....

Uniform attractors in sup-norm for semi linear parabolic problem and application to the robust stability theory

Oleksiy Kapustyan, Olena Kapustian, Oleksandr Stanzytskyi, Ihor Korol (2023)

Archivum Mathematicum

In this paper we establish the existence of the uniform attractor for a semi linear parabolic problem with bounded non autonomous disturbances in the phase space of continuous functions. We applied obtained results to prove the asymptotic gain property with respect to the global attractor of the undisturbed system.

Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu

Francy Armao, Dorota Głazowska, Sergio Rivas, Jessica Rojas (2013)

Open Mathematics

We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.

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