论文标题
涉及振荡术语的差分夹杂物
Differential inclusions involving oscillatory terms
论文作者
论文摘要
由外力不平滑的机械问题激励，我们认为差分包含问题\ [\ begin {case} -ΔU（x）\ in \ partial f（u（x））+λ\ partial g（u（x））\ \ \ \ \ \ \ \ \ \ mbox {in} \ω\ newline u \ geq 0 \ \ mbox {in} \ω\ newline u = 0 \ \ \ mbox {on} \ \partialΩ， \ end {cases} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {（{{\ mathcal d}_λ）} \]其中$ω\ subset {\ mathbb r}^n $是一个有界的开放域，$ \ partial f $和$ \ partial g $站立于本地Lipschitz函数的广义梯度$ f $ and $ g $。在本文中，每当$（{\ Mathcal d}_λ）$的解决方案数量时，每当$ \ partial f $ oscillates附近附近/infinity oscillates和$ \ partial g $时，分别是Origin/Infinity的订单$ P> 0 $。我们的结果扩展了克里斯蒂利和莫罗萨努的几个方面[J.数学。 Pures Appl。，2010年]。
Motivated by mechanical problems where external forces are non-smooth, we consider the differential inclusion problem \[ \begin{cases} -Δu(x)\in \partial F(u(x))+λ\partial G(u(x))\ \mbox{in}\ Ω\newline u\geq 0\ \mbox{in}\ Ω\newline u= 0\ \mbox{on}\ \partialΩ, \end{cases} \ \ \ \ \ \ \ \ \ \ \ \ {({\mathcal D}_λ)} \] where $Ω\subset {\mathbb R}^n$ is a bounded open domain, and $\partial F$ and $\partial G$ stand for the generalized gradients of the locally Lipschitz functions $F$ and $G$. In this paper we provide a quite complete picture on the number of solutions of $({\mathcal D}_λ)$ whenever $\partial F$ oscillates near the origin/infinity and $\partial G$ is a generic perturbation of order $p>0$ at the origin/infinity, respectively. Our results extend in several aspects those of Kristály and Moroşanu [J. Math. Pures Appl., 2010].
