Zobrazeno 1 - 10
of 131
pro vyhledávání: '"Zhu Maochun"'
Autor:
Zhang Caifeng, Zhu Maochun
Publikováno v:
Advanced Nonlinear Studies, Vol 24, Iss 3, Pp 616-636 (2024)
The purpose of this paper is three-fold. First, we establish singular Trudinger–Moser inequalities with less restrictive constraint:(0.1)supu∈H1(R2),∫R2(|∇u|2+V(x)u2)dx≤1∫R2e4π1−β2u2−1|x|βdx
Externí odkaz:
https://doaj.org/article/33abcea961bf45e887d46dbdd286d38f
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 385-398 (2023)
Let II be a bounded interval of R{\mathbb{R}} and λ1(I){\lambda }_{1}\left(I) denote the first eigenvalue of the nonlocal operator (−Δ)14{(-\Delta )}^{\tfrac{1}{4}} with the Dirichlet boundary. We prove that for any 0⩽α
Externí odkaz:
https://doaj.org/article/1a20f547110548c78b3b1c04818f9459
Autor:
Li Dongliang, Zhu Maochun
Publikováno v:
Advanced Nonlinear Studies, Vol 22, Iss 1, Pp 711-724 (2022)
The concentration-compactness principle of Lions type in Euclidean space relies on the Pólya-Szegö inequality, which is not available in non-Euclidean settings. The first proof of the concentration-compactness principle in non-Euclidean setting, su
Externí odkaz:
https://doaj.org/article/1bf8badabe9d44e5941125a3a5e03814
Publikováno v:
Advanced Nonlinear Studies, Vol 21, Iss 4, Pp 917-937 (2021)
The concentration-compactness principle for the Trudinger–Moser-type inequality in the Euclidean space was established crucially relying on the Pólya–Szegő inequality which allows to adapt the symmetrization argument. As far as we know, the fir
Externí odkaz:
https://doaj.org/article/1580571396f1419abe1fc5a9725a44ba
Publikováno v:
Advanced Nonlinear Studies, Vol 21, Iss 4, Pp 733-749 (2021)
The main purpose of this paper is to establish the existence of ground-state solutions to a class of Schrödinger equations with critical exponential growth involving the nonnegative, possibly degenerate, potential V:
Externí odkaz:
https://doaj.org/article/cea7b23fb87c45e394d623d994ef3cad
Publikováno v:
Advances in Nonlinear Analysis, Vol 10, Iss 1, Pp 420-449 (2020)
We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1 < p < 2 under controllable growth conditions, as well as natural growth conditions, respectively, in the Heisenberg group. On the basis of a generalization of the techniq
Externí odkaz:
https://doaj.org/article/7aa5a24dacac46b18199d52c058c27b4
Let $F$ be convex and homogeneous of degree $1$, its polar $F^{o}$ represent a finsler metric on $\mathbb{R}^{n}$, and $\Omega$ be any bounded open set in $\mathbb{R}^{n}$. In this paper, we first construct the theoretical structure of anisotropic ha
Externí odkaz:
http://arxiv.org/abs/2310.18848
Let $\Omega\subseteq \mathbb{R}^{4}$ be a bounded domain with smooth boundary $\partial\Omega$. In this paper, we establish the following sharp form of the trace Adams' inequality in $W^{2,2}(\Omega)$ with zero mean value and zero Neumann boundary co
Externí odkaz:
http://arxiv.org/abs/2308.16347
In this paper, we will solve this uniqueness problem of positive solutions to the following equations of exponential growth: \begin{equation*} \begin{cases} -\Delta u =\lambda ue^{u^2},\quad\quad & x\in B_1\subset \mathbb{R}^2,\\ u>0, & x\in B_1,\ \\
Externí odkaz:
http://arxiv.org/abs/2210.16999
Recently, the authors of the current paper established in [9] the existence of a ground-state solution to the following bi-harmonic equation with the constant potential or Rabinowitz potential: \begin{equation} (-\Delta)^{2}u+V(x)u=f(u)\ \text{in}\ \
Externí odkaz:
http://arxiv.org/abs/2108.06301