differential equations with applications 中文意思是什麼

differential equations with applications 解釋
微分方程及應用
  1. Finally, some properties of limits set of the solution of the dde with local monotone in the delay term are given. moreover, using the above discrete lyapunov functional, we prove that the poincare - bendixson theorem holds for some solutions of this dde. in chapter 4, detail analysis of the global attractor for three particular classes of delay differential equations in concrete applications are given

    最後，給出了最終落在時滯項局部單調范圍內的解的極限集的若干性質，並給出了類似於poincare一bendixson定理的結論及其證明，這些結論的證明盡管與mallet一paret的證明方法相似，但是本文的結論將他有關全局單調的理論推廣到局部單調中去了。
  2. As the applications of mixed monotone operators theory, some classes of equations are considered. some initial value problems and boundary value problems for mixed monotone nonlinear impulsive integro - differential equations and nonlinear elliptic equations are discussed. some known results are generalized under weak conditions. and initial value problems and periodic boundary value problems for mixed monotone nonlinear impulsive evolution equations are discussed by mixed monotone operators theory with considering the main properties of operator semigroup. the sufficient and necessary conditions for existence and uniqueness of their solution and coupled solution are obtained

    作為混合單調運算元理論的應用，本章討論了非線性混合單調脈沖積微分方程和混合單調非線性橢圓方程方面的一些問題，不同程度地削弱了原有的條件，推廣了已知的結果；還利用錐理論並結合運算元半群的性質及其主要特徵討論了非線性脈沖發展方程初值問題、周期邊值問題，給出了混合單調非線性脈沖發展方程的耦合周期解以及存在唯一解的充要條件。
  3. The second part of this paper is concerned with the theory of retarded functional differential equations ( rfdes ) and applications to the existence of positive periodic solutions of rfdes

    本文的第二第二部分著重討論一類滯后型泛函微分方程（ rfdes ）正周期解的存在性。
  4. The study on the stability switches of functional differential difference equations is an important research branch of the stability theories, which of both the theory and its applications has broad prospects. the first part of this paper, chapter 2 and 3, deals with the stability switches for two classes of retarded differential difference systems, respectively. by analyzing the characteristic roots of characteristic equations, some algebraic criteria of stability switches are established, which are useful and easy to verify

    穩定性開關是泛函微分方程穩定性理論中的一個重要分支，無論是理論本身還是它的應用都有廣泛的前景，本文的第一部分（第2章、第3章）分別討論兩類二階滯后型微分差分系統的穩定性開關，通過分析特徵方程的特徵根，我們給出了存在穩定性開關現象的實用而又易於驗證的代數判據，並利用計算機模擬驗算了一個具體例子。
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