AKTUALNE TYTUŁY
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Czasopisma naukowe, biuletyny aktulnie wydawane (roczniki, numery i artykuły).
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Item type:Journal Issue, Opuscula Mathematica2026 - Vol. 46 - No. 3Item type:Article, Access status: Open Access , Existence of solutions for a doubly critical Schrödinger-Poisson system on the first Heisenberg group(Wydawnictwa AGH, 2026) Ma, Xueyan; Shi, Shaoyun; Song, YueqiangThis work is devoted to the study of a class of Schrödinger-Poisson system with doubly critical growth on the first Heisenberg group. Utilizing the concentration-compactness principle associated with classical Sobolev space on the Heisenberg group and mountain pass theorem, we prove that the system admits multiple nontrivial solutions.Item type:Article, Access status: Open Access , On a relation between growth estimates and Harnack inequalities for quasilinear elliptic equations with nonlinear lower order terms(Wydawnictwa AGH, 2026) Hirata, KentaroWe investigate a relation between the Harnack inequalities and the (a priori) growth estimates for positive solutions of quasilinear elliptic equations with nonlinear terms involving the solution and its gradient in an arbitrary domain in $\mathbb{R}^N$.Item type:Article, Access status: Open Access , A priori estimates and existence of positive solutions for elliptic problems under integral Neumann boundary conditions(Wydawnictwa AGH, 2026) Corrêa, Francisco J.S.A.; Figueiredo, Giovany M.; Morbach, JoelmaIn this paper, we establish a priori estimates and existence of positive solutions for elliptic problems under integral Neumann boundary conditions.Item type:Article, Access status: Open Access , Comparison theorems for property (B) of the third-order differential equations with deviating arguments(Wydawnictwa AGH, 2026) Džurina, Jozef; Baculíková, BlankaThe aim of this paper is to introduce a new comparison theorem (in both delayed and advanced cases) that allows us to investigate the properties of third-order differential equations with quasi-derivatives $(r_{1}(t)(r_{2}(t)y'(t))')'-p(t)y(\tau(t))=0$ using the following simpler differential equations $(r(t)(r(t)z'(t))')'-p(t)z(\tau(t))=0$ and $y'''(t)-q(t)y(\sigma(t))=0.$ The obtained comparison principles allow for the immediate transcription of the oscillatory results known for the simpler equations into studied equation with quasi-derivatives. The progress achieved will be illustrated through several examples.Item type:Article, Access status: Open Access , Normalized ground states for a $p$-Laplacian system in the mass super-critical case(Wydawnictwa AGH, 2026) Tao, Yuhang; Zhang, JianjunIn this paper, we study the existence of positive normalized solutions to the following $p$-Laplacian system: $\begin{cases} -\Delta_p u+\lambda_1u^{p-1}=\mu_1u^{m_1-1}+\beta r_1u^{r_1-1}v^{r_2}&\text{in }\mathbb{R}^N,\\ -\Delta_p v+\lambda_2v^{p-1}=\mu_2v^{m_2-1}+\beta r_2u^{r_1}v^{r_2-1}&\text{in }\mathbb{R}^N,\\ \int_{\mathbb{R}^N}|u|^p=a, \quad \int_{\mathbb{R}^N}|v|^p=b,\end{cases}$ where $1\lt p\lt N$, $\mu_1,\mu_2,\beta,a,b\gt 0$ are prescribed, $\lambda_1,\lambda_2 \in \mathbb{R}$ are known as the Lagrange multiplier, $\Delta_p u= \mathrm{div} (|\nabla u|^{p-2} \nabla u)$ denotes the $p$-Laplacian operator. We prove the existence of positive solutions for the coupled purely mass super-critical case (i.e., $\frac{p^2}{N}+p\lt m_1,m_2,r_1 + r_2\lt p^*$) by a minimization argument based on a closed ball and the Pohozaev constraint.Item type:Article, Access status: Open Access , On mixed local-nonlocal Sobolev-type inequalities and their connection with singular equations in the Heisenberg group(Wydawnictwa AGH, 2026) Garain, PrashantaIn this work, we establish a mixed local-nonlocal Sobolev-type inequality in the Heisenberg group and demonstrate that its extremals coincide with solutions to the corresponding mixed local-nonlocal singular $p$-Laplace equations. We further show that these inequalities serve as a necessary and sufficient condition for the existence of weak solutions to the associated singular problems. Notably, the same characterization remains valid in both the purely local and purely nonlocal settings. Our results thus provide a unified framework linking the existence theory for singular equations across local, nonlocal, and mixed regimes.Item type:Article, Access status: Open Access , Normalized solutions for planar Schrödinger-Poisson system with critical exponential growth and nonlocal interaction(Wydawnictwa AGH, 2026) Wei, Chenlu; Chen, Sitong; Shu, MuhuaThis paper focuses on the following planar Schrödinger-Poisson system with critical exponential growth and nonlocal interaction $\begin{cases}-\Delta u+\lambda u+\mu(\log|\cdot|*u^2)u = \gamma \left( I_\alpha * |u|^q \right) |u|^{q-2} u+\left(e^{u^2}-1-u^2\right)u, & x\in \mathbb{R}^2, \\ \displaystyle \int_{\mathbb{R}^2}u^2\mathrm{d}x=c,\end{cases}$ where $c\gt 0$, $\mu,\gamma\gt 0$, $\lambda \in \mathbb{R}$ appears as a Lagrange multiplier, $\alpha \in (0,2)$, $1+\frac{\alpha}{2} \leq q \lt +\infty$, $I_\alpha:\mathbb{R}^2\to\mathbb{R}$ denotes the Riesz potential and $1+\frac{\alpha}{2}$ is the lower critical exponent with respect to the Hardy-Littlewood-Sobolev inequality. Through delicate energy estimates, under explicit conditions on $c$, we prove the existence of two normalized solutions: one is a local minimizer and the other is of mountain-pass type. The presence of the logarithmic kernel and the competition between the two nonlocal terms necessitates the development of new tools to address the loss of compactness caused by the critical exponential growth, for which the variational techniques developed for the local problem are no longer applicable. Our work not only generalizes the special case $\gamma=0$, but also provides an analytical approach that is applicable to more $L^2$-constrained problems with competing nonlocal terms modelling long-range attraction in particle physics.Item type:Journal Issue, Biuletyn AGH : magazyn informacyjny Akademii Górniczo-Hutniczej2026 - Nr 217 (kwiecień)Item type:Journal Issue, Biuletyn AGH : magazyn informacyjny Akademii Górniczo-Hutniczej2026 - Nr 218 (maj)