非线性二阶多值边值问题
Nonlinear second-order multivalued boundary value problems
摘要：
本文研究了含有一般向量$p$ -Laplacian，集值极大单调算子和非线性多值边值条件的二阶微分包含问题.我们的框架是一般的和统一的，包括梯度系统，发展变分不等式和经典的边值问题，即Dirichlet，Neumann和周期问题。使用的概念和技术，从非线性算子理论和多值分析，我们得到的“凸”和“非凸”的问题的解决方案。最后，我们提出了特殊利益的情况下，适合我们的框架，说明我们的结果的一般性。
英文摘要：
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the `convex' and `nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.
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