论文标题
通过动态方法存在解决一类非局部问题的解决方案
Existence of solution for a class of nonlocal problem via dynamical methods
论文作者
论文摘要
在本文中，我们使用动力学方法来确定一类非局部问题的非平凡解决方案的存在，用于$ \ left \ left \ {\ oken {array} {array} {l} {l} {x，x，\int_Ωg（x，\int_Ωg（u） cm} x \ in \partialΩ，\ end {array} \ right。 \ leqno {（p）} $$其中$ω\ subset \ mathbb {r}^n \，（n \ geq 2）$是一个平稳的界面域，$ a：\overlineΩ\ times \ times \ times \ times \ times \ mathbb {r} \ mathbb {r} $是满足某些技术条件的$ c^1 $ functions。
In this paper we use the dynamical methods to establish the existence of nontrivial solution for a class of nonlocal problem of the type $$ \left\{\begin{array}{l} -a\left(x,\int_Ωg(u)\,dx \right)Δu =f(u), \quad x \in Ω\\ u=0, \hspace{2 cm} x \in \partial Ω, \end{array}\right. \leqno{(P)} $$ where $Ω\subset \mathbb{R}^N \, ( N \geq 2)$ is a smooth bounded domain and $a:\overlineΩ \times \mathbb{R} \to \mathbb{R}$ and $g,f: \mathbb{R} \to \mathbb{R}$ are $C^1$-functions that satisfy some technical conditions.
