H-半变分不等式的非线性扰动与分数阶问题

This project studies fractional order and nonlinear perturbation problems of hemivariational inequalities, which involve nonlocal, noncoercive, nonconvex, multi-valued and nondifferential properties. We mainly consider the well-posedness of nonlinear perturbation of elliptic hemivariational inequalities and evolutional hemivariational inequalities with Cauchy, periodic or anti-periodic problems, including existence ,uniqueness(or multiplicity) and stability of solutions, the dependent relationship between sulutions and nonlinear perturbations. Furthermore, we also consider existence, uniqueness (or multiplicity) and stability of Cauchy, periodic and anti-periodic problems of fractional hemivariational inequalities (in this project, we only deal with fractional derivatives with time t) . We try to apply our results to mechanical models so that people could have a sound grip of mechanical problems.

本项目研究涉及非局部、非强制、非凸、多值和不可微特征的H-半变分不等式分数阶和非线性扰动问题。研究具非线性扰动的椭圆型H-半变分不等式问题解的适定性；具有非线性扰动的发展型H-半变分不等式的Cauchy问题、周期问题和反周期问题解的存在性、唯一（或多解）性及稳定性。研究扰动项与相应H-半变分不等式解（集）之间依赖关系。进一步研究（该项目暂只考虑关于时间t的）分数阶H-半变分不等式的Cauchy问题、周期问题和反周期问题解的存在性、唯一性及稳定性。将我们获得的理论成果应用到力学模型。从而，更加深刻理解这类力学问题。

本项目的研究成果涉及非局部、非强制、非凸、多值和不可微特征的H-半变分不等式非线性扰动问题以及分数阶问题。在适当的条件下，证明了具非线性扰动的椭圆型H-半变分不等式问题解的适定性；并得到了具有非线性扰动的发展型H-半变分不等式的Cauchy 问题、周期问题和反周期问题解的存在性、唯一（或多解）性及稳定性。建立了扰动项与相应H-半变分不等式解（集）之间某种依赖关系。还进一步研究了关于时间t 的分数阶H-半变分不等式的Cauchy 问题、周期问题和反周期问题解的存在性、唯一性及稳定性。将我们获得的理论成果应用到几类力学模型。更加深刻理解了这类力学问题。