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数学学科现代分析及其应用研究所(2020非线性分析与偏微分方程系列报告会三十四)

发布者:付慧娟   发布时间:2020-12-24  浏览次数:160


报告题目66Maximal 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:1224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


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