OPUSCULA MATHEMATICA
Permanent URI for this communityhttps://repo.agh.edu.pl/handle/AGH/102755
- Adres wydawniczy: Kraków : Wydawnictwa AGH, 2005-
- O czasopiśmie: http://www.opuscula.agh.edu.pl/
- ISSN: 1232-9274 e-ISSN: 2300-6919
- DOI: http://dx.doi.org/10.7494/OpMath
The journal Opuscula Mathematica publishes original research articles that are of significant importance in all areas of Discrete Mathematics, Functional Analysis, Differential Equations, Mathematical Physics, Nonlinear Analysis, Numerical Analysis, Probability Theory and Statistics, Theory of Optimal Control and Optimization, Financial Mathematics and Mathematical Economic Theory, Operations Research, and other areas of Applied Mathematics.
New! Aktualny numer: 2026 - Vol. 46 - No. 1
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Item type:Article, Access status: Open Access , Galerkin-type minimizers to a competing problem for (p, q)-Laplacian with variable exponents(Wydawnictwa AGH, 2026) Zhang, Zhenfeng; Ghasemi, Mina; Vetro, CalogeroThis study focuses on a sequence of approximate minimizers for the functional \[J(u)=\int\limits_{\Omega}\sum\limits_{i=1}^{N}\frac{1}{p_{i}(x)}\bigg|\frac{\partial u}{\partial x_{i}}\bigg|^{p_{i}(x)}dx-\mu\int\limits_{\Omega}\sum\limits_{i=1}^{N}\frac{1}{q_{i}(x)}\bigg|\frac{\partial u}{\partial x_{i}}\bigg|^{q_{i}(x)}dx-\int\limits_{\Omega} F(u(x))dx,\] where \(\Omega\subset\mathbb{R}^N\) (\(N\geq 3\)) is a bounded domain, and \(p_i,q_i\in C(\overline{\Omega})\) with \(1\lt p_i,q_i\lt +\infty\) for all \(i \in \{1,\ldots,N\}\). We establish the convergence result to the infimum of \(J(u)\) when \(F:\mathbb{R}\to\mathbb{R}\) is a locally Lipschitz function of controlled growth, following the Galerkin method. As an application, we establish the existence of solutions to a class of Dirichlet inclusions associated to the functional.Item type:Article, Access status: Open Access , A short note on Harnack inequality for k-Hessian equations with nonlinear gradient terms(Wydawnictwa AGH, 2026) Mohammed, Ahmed; Porru, GiovanniIn this short note we study a Harnack inequality for \(k\)-Hessian equations that involve nonlinear lower-order terms which depend on the solution and its gradient.Item type:Article, Access status: Open Access , Calderón-Hardy type spaces and the Heisenberg sub-Laplacian(Wydawnictwa AGH, 2026) Rocha, PabloFor \(0 \lt p \leq 1 \lt q \lt \infty\) and \(\gamma \gt 0\), we introduce the Calderón-Hardy spaces \(\mathcal{H}^{p}_{q,\gamma}(\mathbb{H}^{n})\) on the Heisenberg group \(\mathbb{H}^{n}\), and show for every \(f \in H^{p}(\mathbb{H}^{n})\) that the equation \[\mathcal{L}F=f\] has a unique solution \(F\) in \(\mathcal{H}^{p}_{q,2}(\mathbb{H}^{n})\), where \(\mathcal{L}\) is the sub-Laplacian on \(\mathbb{H}^{n}\), \[1 \lt q \lt \frac{n+1}{n} \quad \text{and} \quad (2n+2)\left(2+\frac{2n+2}{q}\right)^{-1} \lt p \leq 1.\]Item type:Article, Access status: Open Access , Parametric formal Gevrey asymptotic expansions in two complex time variable problems(Wydawnictwa AGH, 2026) Chen, Guoting; Lastra, Alberto; Malek, StéphaneThe analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an auxiliary problem in the Borel plane overcomes the absence of adequate domains which would guarantee summability of the formal solution. Moreover, several exponential decay rates of the difference of analytic solutions with respect to the perturbation parameter at the origin are observed, leading to several asymptotic levels relating the analytic and the formal solutionItem type:Article, Access status: Open Access , Wintner-type asymptotic behavior of linear differential systems with a proportional derivative controller(Wydawnictwa AGH, 2026) Ishibashi, KazukiThis study investigated the asymptotic behavior of linear differential systems incorporating a proportional derivative-type (PD) differential operator. Building on the classical asymptotic convergence property of Wintner, a generalized Wintner-type asymptotic result was established for such systems. The proposed framework encompasses a wide class of time-varying coefficient matrices and extends classical asymptotic theory to equations governed by PD operators. An illustrative example is presented to demonstrate the applicability of the proposed theoremItem type:Journal Volume, Opuscula MathematicaVol. 46 (2026)Item type:Journal Issue, Opuscula Mathematica2026 - Vol. 46 - No. 1Item type:Article, Access status: Open Access , From set-valued dynamical processes to fractals(Wydawnictwa AGH, 2025) Guzik, Grzegorz; Kleszcz, GrzegorzWe present a general theory of topological semiattractors and attractors for set-valued semigroups. Our results extend and unify those previously obtained by Lasota and Myjak. In particular, we naturally generalize the concept of semifractals for the systems acting on Hausdorff topological spaces. The main tool in our analysis is the notion of topological (Kuratowski) limits. We especially focus on the forward asymptotic behavior of discrete set-valued processes generated by sequences of iterated function systems. In this context, we establish sufficient conditions for the existence of fractal-type limit sets.Item type:Article, Access status: Open Access , A comprehensive review on the existence of normalized solutions for four classes of nonlinear elliptic equations(Wydawnictwa AGH, 2025) Chen, Sitong; Tang, XianhuaThis paper provides a comprehensive review of recent results concerning the existence of normalized solutions for four classes of nonlinear elliptic equations: Schrödinger equations, Schrödinger-Poisson equations, Kirchhoff equations, and Choquard equationsItem type:Article, Access status: Open Access , Corrigendum to "Nontrivial solutions for Neumann fractional p-Laplacian problems" [Opuscula Math. 45, no. 5 (2025), 623-645](Wydawnictwa AGH, 2025) Li, Chun; Mugnai, Dimitri; Zhao, Tai-JinWe correct some misprints in [Nontrivial solutions for Neumann fractional p-Laplacian problems, Opuscula Math. 45, no. 5 (2025), 623-645]