Bubbling nodal solutions for a large perturbation of the Moser-Trudinger equation on planar domains
Bubbling nodal solutions for a large perturbation of the Moser-Trudinger equation on planar domains
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平面域上 Moser-Trudinger 方程大扰动的冒泡节点解
DOI：
10.1007/s00208-020-01975-w
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发表时间：
2021
影响因子：
1.4
通讯作者：
Angela Pistoia
中科院分区：
文献类型：
--
作者：
Massimo Grossi;Gabriele Mancini;Daisuke Naimen;Angela Pistoia
本文研究了问题$$\开始{aligned} -\Delta u = \lambda u e^{u^2+| u| ^p} \quad \text { in }\quad \Omega，\quad u = 0 \quad \text { on }\partial \Omega，\end{aligned}$$其中是有界光滑域，如果是一个球，它是已知的情况下定义了一个临界阈值之间的存在和不存在的径向对称的符号变化的解决方案。本文构造了一类问题的节点解的爆破族，当是一个任意区域且足够小时。据我们所知，这是第一次在非对称区域上构造Moser-Trudinger临界方程的变号解。
In this work we study the existence of nodal solutions for the problem $$\begin{aligned} -\Delta u = \lambda u e^{u^2+|u|^p} \quad \text { in }\quad \Omega ,\quad u = 0 \quad \text { on }\partial \Omega , \end{aligned}$$whereis a bounded smooth domain and. Ifis a ball, it is known that the casedefines a critical threshold between the existence and the non-existence of radially symmetric sign-changing solutions. In this work we construct a blowing-up family of nodal solutions to such problem as, whenis an arbitrary domain andis small enough. As far as we know, this is the first construction of sign-changing solutions for a Moser–Trudinger critical equation on a non-symmetric domain.