向量值柯西问题的适定性

设A为复Banach空间X上的稠定闭算子.我们证明了若抽象柯西问题具有C-适定性,则{λ∈C:Reλ≥0）　ρ（A）且存在C>0,使得任给λ∈C,Reλ≥0,都有（λ-A）-1≤C/1+　λ.因而A必为X上某一有界解析半群的无穷小生成元.对于定义在有限区间[0,T]上的抽象柯西问题,我们亦得到了类似的结果.     

Multiplicity Results for Second Order Non-Autonomous Singular Dirichlet Systems

In this paper, we establish multiplicity results for second order non-autonomous singular Dirichlet systems. The proof is based on a well-known fixed point theorem in cones, and an existence principle proved in Agarwal and O’Regan (J. Differ. Equ. 175:393–414, 2001), which was established using a nonlinear alternative of Leray-Schauder type. Truncation techniques play an important role in the analysis. Some recent results in the literature are generalized and improved.     

Regularity Theory for Second Order Integro-PDEs

This paper is concerned with higher Hölder regularity for viscosity solutions to non-translation invariant second order integro-PDEs, compared to Mou (2018). We first obtain C^1,α regularity estimates for fully nonlinear integro-PDEs. We then prove the Schauder estimates for solutions if the equation is convex.

     

一类二阶非自治Hamilton系统的周期解

在线性增长和次线性增长条件下,利用临界点理论中的极小作用原理和鞍点定理,研究了二阶非自治Hamilton系统周期解的存在性问题,获得了一些新的可解性条件．     

Second Order Regularity for the A-Laplace Operator

In this paper we establish second order regularity for the quasilinear elliptic equation Δ _A u =  f, where Δ _A is the so called A-Laplace operator.     

High Order Regularity for Interface Problems

Interface problems for second order elliptic partial differential equations are studied. We prove that each weak solution can be decomposed into two parts near singular points, one of which is a linear combination of some particular solutions,and the other one belongs to H where s≥2 is arbitrary.     

Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

This paper presents error estimates in both an energy norm and the $L^2$-norm for the weak Galerkin (WG) finite element methods for elliptic problems with low regularity solutions. The error analysis for the continuous Galerkin finite element remains same regardless of regularity. A totally different analysis is needed for discontinuous finite element methods if the elliptic regularity is lower than H-1.5. Numerical results confirm the theoretical analysis.     

一类二阶非自治迭代微分方程的初值问题

本文研究二阶非自治迭代泛函微分方程x＇＇（t）=a（t）x（t）+b（t）x（x（t））的强解的存在性及其性态,给出了过区域{（t,x）|0相似文献   

First Order LSFEM for Second Order Hyperbolic Problems

In the last years the interest in least squares finite element methods has grown due to some interesting properties of these methods (cf. the monographs [1], [2]). While for many elliptic problems the theoretical background has been established, only a few articles analyse least squares methods for transient problems. In this article some new stability estimates for the least squares method for the wave equation in 1 and 2 dimensions are derived. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Second Order Cones for Maximal Monotone Operators via Representative Functions

It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T, in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the Graph T. In particular we obtain formula for the proto-derivative, as well as its polar, the normal cone to the graph of T. First order derivatives are shown to be useful in recognising points of single-valuedness of T. We show that a strong form of proto-differentiability to the graph of T, is often associated with single valuedness of T. The second author’s research was funded by NSERC and the Canada Research Chair programme, and the first author’s by ARC grant number DP0664423. This study was commenced between August and December 2005 while the first author was visiting Dalhousie University.     

算子值傅里叶乘子与向量值边值问题最大正则性

向量值L^p空间上的算子值傅里叶乘子由于L．Weis在2000年的重要工作而成为泛函分析的热点之一，其对R-有界性创造性的应用使这个领域的研究耳目一新，新的结果层出不穷．本文的目的是介绍算子值傅里叶乘子的这些最新进展，以及它们在向量值边值问题最大正则性方面的应用．包括N．J．Kalton和G．Lancien给出的关于L^p-最大正则性的反例．Besov空间和Triebel空间上的算子值傅里叶乘子以及在Besov空问和Triebel空间意义下的最大正则性也是我们要介绍的内容．     

The Dirichlet and Regularity Problems for Some Second Order Linear Elliptic Systems on Bounded Lipschitz Domains

In this paper, we investigate divergence-form linear elliptic systems on bounded Lipschitz domains in \(\mathbb {R}^{d+1}, d \ge 2\), with L² boundary data. The coefficients are assumed to be real, bounded, and measurable. We show that when the coefficients are small, in Carleson norm, compared to one that is continuous on the boundary, we obtain solvability for both the Dirichlet and regularity boundary value problems given that the coefficients satisfy a certain “pseudo-symmetry” condition.     

The Kneser Property for the Second Order Functional Abstract Cauchy Problem

In this work we establish existence of mild solutions for a class of abstract semi-linear functional differential equations of second order and we prove that the set consisting of the mild solutions for these problems is connected.     

Quadratic Eigenvalue Problems for Second Order Systems

We consider the spectral structure of a quadratic second order system boundary-value problem. In particular we show that all but a finite number of the eigenvalues are real and semi-simple. We develop the eigencurve theory for these problems and show that the order of contact between an eigencurve and the parabola gives the Jordan chain associated with the eigenvector corresponding to that eigencurve. Following this we use our knowledge of the eigencurves to obtain eigenvalue asymptotics. Finally the completeness of the eigenfunctions is studied using operator matrix techniques. It should be noted here that the usual left definiteness assumptions have been overcome in this study.     

Cauchy Problem to a Type of Second Order Differential-iterative Equation

Abstract The paper studies the behavior and existence of strong solutions to the second or-der functional-iterative differential equation     

C-cosine Operator Functions and the Second Order Abstract Cauchy Problem

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一类二阶迭代泛函微分方程的初值问题(英文)

本文利用Schauder不动点定理,首次研究了一类二阶迭代泛函微分方程x″(t)= x(x(t)),满足初始条件:x′(σ)= 0;x(σ)= σ的强解的存在性及其性态.     

完全二阶抽象Cauchy问题的C-适定性及其应用

在本文中,我们给出了算子矩阵生成指数有界的半群的充分必要条件,其中A0,A1为完全二阶抽象柯西问题（ACP2）的系数算子,并讨论了它与（ACP2）在某种意义下的C-适定性之间的关系．最后,我们应用此结果及［3］中的结论讨论了一类具有应用背景的完全二阶抽象柯西问题的C-适定性．     

Nonlinear Boundary Value Problems for Second Order Differential Inclusions

In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form x ↦ a(x, x′)′. In this problem the maximal monotone term is required to be defined everywhere in the state space ℝ^N. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ↦ (a(x)x′)′. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side.