Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2020
Volume
Vol. 40
Number
No. 1
Description
The issue is dedicated to Professor Dušan D. Repovš on the occasion of his 65th birthday.
Journal Volume
Opuscula Mathematica
Vol. 40 (2020)
Projects
Pages
Articles
On some convergence results for fractional periodic Sobolev spaces
(Wydawnictwa AGH, 2020) Ambrosio, Vincenzo
In this note we extend the well-known limiting formulas due to Bourgain-Brezis-Mironescu and Maz'ya-Shaposhnikova, to the setting of fractional Sobolev spaces on the torus. We also give a $\Gamma$-convergence result in the spirit of Ponce. The main theorems are obtained by using the nice structure of Fourier series.
Some multiplicity results of homoclinic solutions for second order Hamiltonian systems
(Wydawnictwa AGH, 2020) Barile, Sara; Salvatore, Addolorata
We look for homoclinic solutions $q:\mathbb{R} \rightarrow \mathbb{R}^N$ to the class of second order Hamiltonian systems $-\ddot{q} + L(t)q = a(t) \nabla G_1(q) - b(t) \nabla G_2(q) + f(t) \quad t \in \mathbb{R}$ where $L: \mathbb{R}\rightarrow \mathbb{R}^{N \times N}$ and $a,b: \mathbb{R}\rightarrow \mathbb{R}$ are positive bounded functions, $G_1, G_2: \mathbb{R}^N \rightarrow \mathbb{R}$ are positive homogeneous functions and $f:\mathbb{R}\rightarrow\mathbb{R}^N$. Using variational techniques and the Pohozaev fibering method, we prove the existence of infinitely many solutions if $f\equiv 0$ and the existence of at least three solutions if $f$ is not trivial but small enough.
On solvability of elliptic boundary value problems via global invertibility
(Wydawnictwa AGH, 2020) Bełdziński, Michał; Galewski, Marek
In this work we apply global invertibility result in order to examine the solvability of elliptic equations with both Neumann and Dirichlet boundary conditions.
On the regularity of solution to the time-dependent p-Stokes system
(Wydawnictwa AGH, 2020) Berselli, Luigi C.; Růžička, Michael
In this paper we consider the time evolutionary $p$-Stokes problem in a smooth and bounded domain. This system models the unsteady motion or certain non-Newtonian incompressible fluids in the regime of slow motions, when the convective term is negligible. We prove results of space/time regularity, showing that first-order time-derivatives and second-order space-derivatives of the velocity and first-order space-derivatives of the pressure belong to rather natural Lebesgue spaces.
Nonhomogeneous equations with critical exponential growth and lack of compactness
(Wydawnictwa AGH, 2020) Figueiredo, Giovany M.; Rădulescu, Vicenţiu D.
We study the existence and multiplicity of positive solutions for the following class of quasilinear problems $-\operatorname{div}(a(|\nabla u|^{p})| \nabla u|^{p-2}\nabla u)+V(\epsilon x)b(|u|^{p})|u|^{p-2}u=f(u) \qquad\text{ in } \mathbb{R}^N,$ where $\epsilon$ is a positive parameter. We assume that $V:\mathbb{R}^N \to \mathbb{R}$ is a continuous potential and $f:\mathbb{R}\to\mathbb{R}$ is a smooth reaction term with critical exponential growth.