Browsing by Subject "compactness"

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Access status: Open Access ,
Compact generalized weighted composition operators on the Bergman space
(2017) Hu, Qinghua; Zhu, Xiangling
We characterize the compactness of the generalized weighted composition operators acting on the Bergman space.
Access status: Open Access ,
Existence of critical elliptic systems with boundary singularities
(2013) Yang, Jianfu; Zhou, Yimin
In this paper, we are concerned with the existence of positive solutions of the following nonlinear elliptic system involving critical Hardy-Sobolev exponent $\begin{equation*}\label{eq:1}(*) \left\{ \begin{array}{lll} -\Delta u= \frac{2\alpha}{\alpha+\beta}\frac{u^{\alpha-1}v^\beta}{|x|^s}-\lambda u^p, & \quad {\rm in}\quad \Omega,\\[2mm] -\Delta v= \frac{2\beta}{\alpha+\beta}\frac{u^\alpha v^{\beta-1}}{|x|^s}-\lambda v^p, & \quad {\rm in}\quad \Omega,\\[2mm] u\gt 0, v\gt 0, &\quad {\rm in}\quad \Omega,\\[2mm] u=v=0, &\quad {\rm on}\quad \partial\Omega, \end{array} \right. \end{equation*}$ where $N\geq 4$ and $\Omega$ is a $C^1$ bounded domain in $\mathbb{R}^N$ with $0\in\partial\Omega$. $0\lt s \lt 2$, $\alpha+\beta=2^*(s)=\frac{2(N-s)}{N-2}$, $\alpha,\beta\gt 1$, $\lambda\gt 0$ and $1 \lt p\lt \frac{N+2}{N-2}$. The case when 0 belongs to the boundary of $\Omega$ is closely related to the mean curvature at the origin on the boundary. We show in this paper that problem $(*)$ possesses at least a positive solution.
Access status: Restricted ,
Własności spektralne zaburzonych półgrup i ich zastosowania w teorii transportu
(Data obrony: 2012-07-10) Janiczko, Tomasz
Wydział Matematyki Stosowanej