论文标题
非线性变化不平等和应用的耦合系统
Coupled systems of nonlinear variational inequalities and applications
论文作者
论文摘要
在本文中，我们研究了由两种变异类型不等式组成的系统的解决方案的存在。每个不平等是根据非线性双方函数$χ$和$ψ$和耦合功能$ b $进行制定的。我们考虑两组假设$ {\ bf（h_χ^i）} $，$ {\ bf（h_ψ^j）} $和$ {\ bf（h_b^k）} $，$ i，$ i，j，j，j，j，k \ in \ in \ in \ in \ {1,2 \} $，如果不这样做，我们的二次限制了，或者是一个限制了一个界限，或者是一个界限。 $χ$，$ψ$或$ b $的假设，从而获得了八种可能性。当约束集无界时，需要施加性条件以确保解决方案的存在。我们提供两个这样的条件。我们考虑非线性耦合功能，而在我们知道的所有论文中，涉及这种类型的不平等系统的耦合函数被假定为双线性并满足某些“ Inf-Sup”条件。在上一节中介绍了由$φ$ -laplace运算符驱动的部分差分包含形式的联系方式。
In this paper we investigate the existence of solutions for a system consisting of two inequalities of variational type. Each inequality is formulated in terms of a nonlinear bifunction $χ$ and $ψ$, respectively and a coupling functional $B$. We consider two sets of assumptions ${\bf (H_χ^i)}$, ${\bf (H_ψ^j)}$ and ${\bf (H_B^k)}$, $i,j,k\in\{1,2\}$ and we show that, if the constraints sets are bounded, then a solution exists regardless if we assumed the first or the second hypothesis on $χ$, $ψ$ or $B$, thus obtaining eight possibilities. When the constraint sets are unbounded a coercivity condition is needed to ensure the existence of solutions. We provide two such conditions. We consider nonlinear coupling functionals, whereas, in all the papers that we are aware of that dealing with such type of inequality systems the coupling functional is assumed bilinear and satisfies a certain "inf-sup" condition. An application, arising from Contact Mechanics, in the form of a partial differential inclusion driven by the $Φ$-Laplace operator is presented in the last section.
