论文标题
梯度系统的替代定理
An alternative theorem for gradient systems
论文作者
论文摘要
在本文中，给定两个Banach空间$ x，y $和a $ c^1 $函数$φ：x \ times y \ to {\ bf r} $，在一般假设下，我们表明，要么$ x \ times y $ $ $ $ $或，对于每个凸起和密集的$ s \ sepseeq y $ y y y $ y $， $φ（\ cdot，\ tilde y）$在$ x $中至少具有三个关键点，其中两个是全球最小值。此外，还提出了对非合件椭圆系统的应用。
In this paper, given two Banach spaces $X, Y$ and a $C^1$ functional $Φ:X\times Y\to {\bf R}$, under general assumptions, we show that either $Φ$ has a saddle-point in $X\times Y$ or, for each convex and dense set $S\subseteq Y$, there is some $\tilde y\in S$ such that $Φ(\cdot,\tilde y)$ has at least three critical points in $X$, two of which are global minima. Also, an application to non-cooperative elliptic systems is presented.
