论文标题
存在一类不确定的变分问题的解决方案，具有不连续的非线性
Existence of solution for a class of indefinite variational problems with discontinuous nonlinearity
论文作者
论文摘要
本文涉及存在以下问题的非平凡解决方案 \ begin {equation} \ left \ {\ begin {aligned} -ΔU + v（x）u＆\ in \ partial_u f（x，u）\; \; \ mbox {a.e。 in} \; \; \ mathbb {r}^{n}，\ nonumber u \ in H^{1}（\ Mathbb {r}^{n}）。 \ end {Aligned} \ right。\ leqno {（p）} \ end {qore}其中$ f（x，t）= \ int_ {0}^{t} f（x，x，s）\，ds $，$ f $是$ \ mathbb {z}^{n}^{n} $ - 周期性的caratheodory函数，$λ= 0 $不属于$ - $ - $ - $ - +v $ v $。在这里，$ \ partial_t f $表示相对于可变$ t $的$ f $的通用梯度。
This paper concerns the existence of a nontrivial solution for the following problem \begin{equation} \left\{\begin{aligned} -Δu + V(x)u & \in \partial_u F(x,u)\;\;\mbox{a.e. in}\;\;\mathbb{R}^{N},\nonumber u \in H^{1}(\mathbb{R}^{N}). \end{aligned} \right.\leqno{(P)} \end{equation} where $F(x,t)=\int_{0}^{t}f(x,s)\,ds$, $f$ is a $\mathbb{Z}^{N}$-periodic Caratheodory function and $λ=0$ does not belong to the spectrum of $-Δ+V$. Here, $\partial_t F$ denotes the generalized gradient of $F$ with respect to variable $t$.
