发展包含是偏微分方程领域里的一个重要的研究课题之一。近年来，对它的研究及应用已有一系列的新成果。本项目将在已有工作的基础上，拟对一类非线性发展包含的反周期解的存在性及其在控制理论中的应用进行研究。具体内容如下：(1) 讨论一类伪单调型发展包含问题反周期解的存在性；(2) 在反周期条件下，对多值项取非凸值的非线性单调型发展包含的Extremal解及其Bang-Bang控制原则进行讨论；(3) H-半变分不等式作为一类特殊的非线性包含问题，我们还将对一类抛物型H-半变分不等式的反周期解问题以及它的反馈控制进行讨论。发展包含和H-半变分不等式在物理学、力学、工程应用、经济学等中具有很广泛的应用。

The evolution inclusion is one of important research subjects in nonlinear partial differential equations. Recently, there are a series of new results obtained about evolution inclusions. Based on the previous work, we will mainly discuss the existence of anti-periodic solutions for a class of nonlinear evolution inclusions and their applications in the control theory in this project. The detailed research contents are as follows: (1) discussing the existence of anti-periodic solutions for a class of pseudomonotone evolution inclusions and hemivariational inequalities of parabolic type; (2) studying the “Bang-Bang” principle and the existence of extremal solutions for nonlinear monotone evolution inclusions with non-convex valued multivalued term under anti-periodic conditions; (3) exploring the relaxation properties of an abstract feedback control system described by parabolic hemivariational inequalities under two different convexification techniques. The subjects investigated in this project have a wide range of applications in physics, mechanics, engineering, economics etc.