论文标题
圆锥上椭圆形问题的基础状态
Ground states of elliptic problems over cones
论文作者
论文摘要
给定反射性Banach Space $ x $，我们考虑一类功能$φ\ in C^1（x，\ re）$在c $ t $ t \ t $ t \ mapstoφ（tu）$，$ t> 0 $的意义上，与$ u \ in x $没有均匀的几何形状，它们的表现不均匀。相反，假设在开放锥$ y \ subset x \ setMinus \ {0 \} $中采用这种统一的行为，我们表明$φ$相对于$ y $具有基态。在一些进一步的条件下，该相对基态是$φ$的（绝对）基态。给出了椭圆方程和系统的几种应用。
Given a reflexive Banach space $X$, we consider a class of functionals $Φ\in C^1(X,\Re)$ that do not behave in a uniform way, in the sense that the map $t \mapsto Φ(tu)$, $t>0$, does not have a uniform geometry with respect to $u\in X$. Assuming instead such a uniform behavior within an open cone $Y \subset X \setminus \{0\}$, we show that $Φ$ has a ground state relative to $Y$. Some further conditions ensure that this relative ground state is the (absolute) ground state of $Φ$. Several applications to elliptic equations and systems are given.
