论文标题
订单理论的多价固定点方法，用于双分支的准差异包含
An Order-Theoretical Multi-Valued Fixed Point Approach to Quasi-Variational Inclusions with Bifunctions
论文作者
论文摘要
我们提出了一个订单理论固定点定理，用于增加适合子苏绝语方法的多估算运算符及其在以下多估的准级变量包含中的应用：让$ω\ subset \ subset \ mathbb r^n $为有界的lipsedipschitz域和$ w = w_0^= w_0^{1，p} {1，p}（ω（ω））$。在W $中查找$ u \，以便对于某些可测量的选择$ f（\ cdot，u，u）$，它保留\ begin \ begin {equination*} \ langle eu，w-u \ rangle + \ rangle + \int_Ω消息 \end{equation*} where $E\colon W \to W^\ast$ is an elliptic Leray-Lions operator of divergence form, $f\colon Ω\times \mathbb R\times \mathbb R \to \mathcal P(\mathbb R)$ is a multivalued bifunction being upper semicontinuous in the second and decreasing in the third参数和$ k（\ cdot，u）$是W $中每个$ u \的凸功能。在数据上的弱假设下，我们将证明每对适当定义的子苏装之间有最小，最大的解决方案。
We present an order-theoretical fixed point theorem for increasing multivalued operators suitable for the method of sub-supersolutions and its application to the following multivalued quasi-variational inclusion: Let $Ω\subset \mathbb R^N$ be a bounded Lipschitz domain and $W = W_0^{1,p}(Ω)$. Find $u\in W$ such that for some measurable selection $η$ of $f(\cdot,u,u)$ it holds \begin{equation*} \langle Eu,w-u\rangle + \int_Ωη(w-u) + K(w,u) - K(u,u) \geq 0\quad\text{for all }w\in W, \end{equation*} where $E\colon W \to W^\ast$ is an elliptic Leray-Lions operator of divergence form, $f\colon Ω\times \mathbb R\times \mathbb R \to \mathcal P(\mathbb R)$ is a multivalued bifunction being upper semicontinuous in the second and decreasing in the third argument, and $K(\cdot,u)$ is a convex functional for each $u\in W$. Under weak assumptions on the data we will prove that there are smallest and greatest solutions between each pair of appropriately defined sub-supersolutions.
