H-半变分不等式的非线性扰动与分数阶问题

项目名称： H-半变分不等式的非线性扰动与分数阶问题

项目编号： No.11271087

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 刘振海

作者单位： 广西民族大学

项目金额： 70万元

中文摘要： 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。

中文关键词： H-半变分不等式；分数阶问题；非线性扰动；非局部问题；解的存在性

英文摘要： 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.

英文关键词： Hemivariational inequalities;；fractional problems；Nonlinear perturbations；Nonlocal problems；Existence of solutions