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pro vyhledávání: '"Elliptic System"'
In this paper, we investigate the following elliptic system with Sobolev critical growth $-\Delta u+P(|y'|,y'')u=u^{2^*-1}+\frac{\beta}{2} u^{\frac{2^*}{2}-1}v^{\frac{2^*}{2}},\ y\in R^N$, $-\Delta v+Q(|y'|,y'')v=v^{2^*-1}+\frac{\beta}{2} v^{\frac{2^
Externí odkaz:
http://arxiv.org/abs/2409.17543
Autor:
Li Bin
Publikováno v:
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 185-206 (2024)
The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of
Externí odkaz:
https://doaj.org/article/eabcf4e01d434a3f9a4dff83d1bfcfad
Autor:
Vitillaro, Enzo
The paper addresses the doubly elliptic eigenvalue problem $$\begin{cases} -\Delta u=\lambda u \qquad &\text{in $\Omega$,}\\ u=0 &\text{on $\Gamma_0$,}\\ -\Delta_\Gamma u +\partial_\nu u =\lambda u\qquad &\text{on $\Gamma_1$,} \end{cases} $$ where $\
Externí odkaz:
http://arxiv.org/abs/2403.19759
Akademický článek
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Akademický článek
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Autor:
Qi, Wanting, Zhang, Xingyong
We are interested in looking for two nontrivial solutions for a class of nonhomogeneous quasilinear elliptic system with sign-changing weight functions and concave-convex nonlinearities on the bounded domain. This kind of quasilinear elliptic system
Externí odkaz:
http://arxiv.org/abs/2312.17426
We consider the following elliptic system with Neumann boundary: \begin{equation} \begin{cases} -\Delta u + \mu u=v^p, &\hbox{in } \Omega, \\-\Delta v + \mu v=u^q, &\hbox{in } \Omega, \\\frac{\partial u}{\partial n} = \frac{\partial v}{\partial n} =
Externí odkaz:
http://arxiv.org/abs/2402.16489
Autor:
Petraszczuk, Bogdan
Inspired by Frehse's [1] 1973 work, we show that his elliptic system $\Delta u = F(u, \nabla u)$ in the plane has bounded weak solutions $u$ with arbitrarily prescribed singular sets.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2402.09224
In this paper, we discuss the existence and uniqueness of coexistence states for a class of non-local elliptic system. This problem models the behaviour of a bacteria and a living nutrient, whose diffusion depends on the population of the bacteria in
Externí odkaz:
http://arxiv.org/abs/2402.02912
Autor:
Qi, Wen-Juan, Sun, Zhao-Min
In this short note, we extend the conservation law of Lamm-Rivi\`ere [Comm. PDEs 2008] for a fourth order elliptic system to supercritical dimensions, under certain Lorentz-Sobolev integrability assumptions on the associated coefficient functions.
Externí odkaz:
http://arxiv.org/abs/2401.15401