【摘要】 本文研究了在Hilbert空间中与极大单调算子族相联系的抽象的二阶发展方程的反周期问题 ,给出了关于算子族 {A(t) :0≤t≤T}的新的假设 ,并在此假设下证明了反周期解的存在性与惟一性 ,推广了已有的结果 .最后给出一个例子说明抽象的反周期问题在非线性偏微分方程中的简单应用 .更多还原

【Abstract】 In this paper we discuss the anti periodic problem for a class of abstract nonlinear second order evolution equations associated with maximal monotone operators in Hilbert spaces and give some new assumptions on operators. We establish the existence and uniqueness of anti periodic solutions,which improve andgeneralize the results that have been obtained.Finally we illustrate the abstract theory by discussing a simple example of an anti periodic problem for nonlinear partial differential equations.更多还原