In Chapter 2, we use Zorn lemma and generalized order set general principle [47] to generalize classical Caristi fixed point theorem, respectively, which weaken the condition that the functional is bounded from below.

在第二章中，我們首先分別利用Zorn引理和推廣的序集一般原理[47]推廣了古典的Caristi不動(dòng)點(diǎn)定理免费看乱伦毛片，削弱了泛函下方有界這個(gè)條件。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我們對(duì)Banach空間中的高階算子微分方程的理論以及相關(guān)理論進(jìn)行了深入研究5566影音先锋在线，解決了由美國(guó)和意大利的四位數(shù)學(xué)家聯(lián)合提出的一個(gè)關(guān)于廣義Wentzell邊界條件下的波動(dòng)方程適定性的公開(kāi)問(wèn)題，恰當(dāng)?shù)囟x了Banach空間中的高階算子微分方程Cauchy問(wèn)題的算子存在族及唯一族cao97，建立了齊次和非齊次高階算子微分方程Cauchy問(wèn)題適定性的判別定理www.狼友视频网站，獲得了關(guān)于高階退化算子微分方程的算子存在族、正則余弦算子族国产一级在视频、正則算子半群毛片.com、Volterra積分方程解算子族的乘積擾動(dòng)和混合擾動(dòng)定理美女福利操一操，得到了關(guān)于以依賴于時(shí)間的二階微分算子為系數(shù)的一大類非自治熱方程非齊次情形下的時(shí)變廣義Wentzell動(dòng)力邊值問(wèn)題的古典解、嚴(yán)格解的最大正則性結(jié)果91精品视频在线无码，獲得了半線性發(fā)展方程非局部Cauchy問(wèn)題廣義解和經(jīng)典解存在唯一的判別條件日韩AV无码久久一区二区，從實(shí)質(zhì)上推廣了現(xiàn)有的相關(guān)結(jié)果；得到了一部分邊緣固定而另一部分附在一粘彈性剛體上的薄板構(gòu)成的混合粘彈性系統(tǒng)的邊界反饋穩(wěn)定化的新穩(wěn)定化定理操人人看日日夜夜人人看操人人看，還建立了一系列其他研究結(jié)果人人人人人人爱。

order bounded set：有序有界集

order 次數(shù) | order bounded set 有序有界集 | order boundedness 有序有界性