报告题目66：Maximal domains of the $(\lambda,\mu)$-parameters to existence of entire positive solutions for singular quasilinear elliptic systems
报 告 人：周家正（巴西利亚大学）
会议时间：12月24日（周四），18：30-19：30
腾讯会议ID: 499 902 793，
https://meeting.tencent.com/s/hpCZDPDmgbwp
摘要：In this paper we establish maximal domains on the real parameters $\lambda,\mu>0$ to existence of $C^{1}(\mathbb{R}^{N})$-entire positive solutions for the quasilinear elliptic system$$\left\{\begin{array}{l}-\Delta_p u = \eta a(x)f_1(u) +\lambda b(x)g_1(u)h_1(v)~in ~ \mathbb{R}^N,\\-\Delta_p v = \theta c(x)f_2(v) + \mu d(x)g_2(v)h_2(u)~in~ \mathbb{R}^N,\\u, v > 0~in~ \mathbb{R}^N,~~ u(x), v(x) \stackrel{|x|\rightarrow\infty}{\longrightarrow} 0,\end{array}\right.
$$ where $\Delta_p$ is the $p-$Laplacian operator with $1 < p< N $ ($3\leq N$); $0<a, b, c, d\in C(\mathbb{R}^{N})$; either $\eta=\theta=1$ or $\eta=\lambda,\theta=\mu$ and $f_i, g_i, h_i~(i=1,2)$ are positive continuous functions that satisfy some technical conditions, which allow $f_{i}$ behaves in a singular way at $0$ and $g_ih_i$ as a $(p-1)$-superlinear term at $0$ and infinity. The main difficulties in approaching our problem come from its non-variational structure, building ordered sub-supersolutions and from the lack of a well-defined spectral theory. By using appropriate truncation, a generalization of the first eigenvalue in $\mathbb{R}^{N}$ and a priori estimates, we are able to prove our principal results.
报告人简介：周家正，巴西利亚大学，教授，主要从事非线性分析及其应用领域的研究。学术成果主要发表于Z. Angew. Math. Phys. Proc. Edinb. Math. Soc. Commun. Contemp. Math. Proc. Roy. Soc. Edinburgh Sect. A. J. Math. Anal. Appl.等国际知名数学杂志上。
邀请人：非线性分析与PDE团队
