论文标题
能量功能和应用的方法
The method of the energy function and applications
论文作者
论文摘要
在这项工作中，我们建立了一种新方法，以查找Banach空格中定义的可区分功能的关键点，该功能属于函数的合适类（$ \ MATHCAL {J} $）。一旦给出了班级的功能性$ j $（$ \ mathcal {j} $），引用方法的核心思想在于定义一个真实变量的真实函数$ζ$，称为{\ it Energy函数}，它与$ j $自然相关，因为在$ζ$中的实际关键点具有$ζ$ j的存在的重要性，而这些Q $ j $ jussigity j $ j $ j $ j $ j $ j $ j $ j $ jusectional j $ j $均具有功能$ $ $ $ $ $ $。结果，我们能够解决一些各种椭圆问题，其相关的能量功能属于（$ \ Mathcal {j} $），并提供类别中的Mountain Pass定理的版本（$ \ Mathcal {J {J} $），该版本允许我们在没有所谓的Ambrosetti-Rabiniitz-rabinowitz条件的情况下获得Mountain Pass Solutions。
In this work, we establish a new method to find critical points of differentiable functionals defined in Banach spaces which belong to a suitable class ($\mathcal{J}$) of functionals. Once given a functional $J$ in the class ($\mathcal{J}$), the central idea of the referred method consists in defining a real function $ζ$ of a real variable, called {\it energy function}, which is naturally associated to $J$ in the sense that the existence of real critical points for $ζ$ guarantees the existence of critical points for the functional $J$. As a consequence, we are able to solve some variational elliptic problems, whose associated energy functional belongs to ($\mathcal{J}$) and provide a version of the mountain pass theorem for functionals in the class ($\mathcal{J}$) that allows us to obtain mountain pass solutions without the so-called Ambrosetti-Rabinowitz condition.
