半线性椭圆方程正解的存在性和唯一性

本文致力于研究半线性椭圆方程正解的存在性,唯一性和非退化性;给出了保证我们所考虑的问题存在正解的一个充要条件;证明了如果某类半线性椭圆问题的正解是唯一的和非退化的,则对问题中的微分算子做小扰动后其正解也是唯一的和非退化的．作为推论,证明了正解的唯一性在区域的小扰动下是不变的．     

具动力边界条件的半线性Kirchhoff方程整体解的不存在性

利用凸性方法得到了具动力边界条件的半线性Kirchhoff方程整体解的不存在性.     

半线性方程组边界层解的存在性

本文利用隐函数定理讨论了含小参数的半线性椭圆方程组边界层解的存在性．     

一类非线性椭圆方程解的存在性

本文讨论了一类无界域上半线性椭圆方程正解的存在性,通过对一类带权索伯列夫空间的深入研究并利用集中紧性的技巧,克服了失去紧性的困难,因此得到了正解的存在性.     

关于线性互补问题解的存在性

讨论线性互补问题解的存在性。证明关于解的唯一性定理。用反例表明:对于线性互补问题解的存在性,"M是半正定矩阵"既不是充分条件,也不是必要条件。     

一类奇异边值问题解的存在性

在非线性项系数无界的情形下，得到了一类半线性椭圆型方程爆破解的存在性。     

一类二阶退化半线性椭圆型方程边值问题的适定性及解的正则性

本文考虑一类二阶退化半线性椭圆型方程边值问题.由椭圆正则化方法建立能量不等式,利用紧性推理,Banach—Saks定理,弱解与强解一致性,解常微分方程,椭圆型方程正则性定理,迭代方法.极值原理和Fredholm—Riesz-Schauder理论,可得相应线性问题适定性及解的高阶正则性;再由Moser引理和Banach不动点定理可得半线性问题解的存在性.这类问题与几何中无穷小等距形变刚性问题密切相关,其高阶正则性解的存在性对几何应用尤为重要.     

一类二阶退化半线性椭圆型方程边值问题的适定性及解的正则性

本文考虑一类二阶退化半线性椭圆型方程边值问题.由椭圆正则化方法建立能量不等式,利用紧性推理,Banach-Saks定理,弱解与强解一致性,解常微分方程,椭圆型方程正则性定理,迭代方法,极值原理和Fredholm-Riesz-Schauder理论,可得相应线性问题适定性及解的高阶正则性;再由Moser引理和Banach不动点定理可得半线性问题解的存在性.这类问题与几何中无穷小等距形变刚性问题密切相关,其高阶正则性解的存在性对几何应用尤为重要.     

一类随机种群方程解的存在性和指数稳定性

首先对一类半线性随机发展方程建立其解的存在性和渐近行为的结果,这类方程的线性部分生成一强连续半群.然后将抽象结果应用于依赖年龄的随机种群方程,获得它的存在性和渐近性质.     

椭圆方程组径向非负解的存在性

应用锥不动点定理证明了圆环中半线性椭圆方程径向非负解的存在性.     

Controllability of Some Nonlinear Systems in Hilbert Spaces

In this paper, several abstract results concerning the controllability of semilinear evolution systems are obtained. First, approximate controllability conditions for semilinear systems are obtained by means of a fixed-point theorem of the Rothe type; in this case, the compactness of the linear operator is assumed. Next, the exact controllability of semilinear systems with nonlinearities having small Lipschitz constants is derived by means of the Banach fixed-point theorem; in this case, the compactness of the operators is not assumed. In both cases, it is proven that the controllability of the linear system implies the controllability of the associated semilinear system. Finally, these abstract results are applied to the controllability of the semilinear wave and heat equations.     

Propagation of Mild Singularities in Higher Dimensional Thermoelasticity

The propagation of mild singularities for the semilinear model of three-dimensional thermoelasticity is studied. It is shown that the propagation picture of such singularities of the solution to the semilinear model coincides with one of the solutions to the corresponding linear model. As a simple consequence of our method, a similar result for the full semilinear Cauchy problem of one-dimensional thermoelasticity is also presented.     

一类边界控制半线性抛物型系统的逼近能控性

本文考虑一类Ｄｉｒｉｃｈｌｅｔ型边界控制半线性抛物型系统，应用半群理论和非线性分析的方法，证明了系统解映射的连续性，给出了系统逼近能控的一个充分条件．对于Ｎｅｕｍａｎｎ型边界控制或混合型边界控制的半线性抛物型系统，可以得到类似的结果．     

Propagation of singularities for Cauchy problems of semilinear thermoelastic systems with microtemperatures

The propagation of singularities of solutions to the Cauchy problem of a semilinear thermoelastic system with microtemperatures in one space variable is studied. First, by using a diagonalization argument of phase space analysis, the coupled thermoelastic system with microtemperatures will be decoupled microlocally. Second, using a classical bootstrap argument, the property of finite propagation speed of singularities for the semilinear thermoelastic system is obtained. Finally, it is also shown that the microlocal weak singularities propagate along the null bicharacteristics of the hyperbolic operators of the coupled semilinear system (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exact Controllability of Semilinear Evolution Systems and Its Application

In this paper, we obtain several abstract results concerning the exact controllability of semilinear evolution systems. First, we prove the null local exact controllability of semilinear first-order systems by means of the contraction mapping principle; in this case, we do not assume any compactness. Next, we derive the global and/or local exact controllability of semilinear second-order systems by means of the Schauder fixed-point theorem; in this case, we assume only the embedding of the related spaces having some compactness, which is reasonable for many concrete problems. Our main result shows that the observability of the dual of the linearized system implies the exact controllability of the original semilinear system. Finally, we apply our abstract results to the exact controllability of the semilinear wave equation.     

Exact null controllability of semilinear integrodifferential systems in Hilbert spaces

Sufficient conditions for exact null controllability of the semilinear integrodifferential systems in Hilbert spaces are obtained. It is shown that under some natural conditions exact null controllability of the semilinear integrodifferential system is implied by the exact null controllability of the corresponding linear system with additive term. An application to partial integrodifferential equations is given.     

Delta-waves for Semilinear Hyperbolic Cauchy Problems

This paper deals with the propagation of strong singularities for constant coefficient semilinear hyperbolic equations and systems. Limits of regularized solutions are computed as the initial data converge to derivatives of Dirac measures on lower dimensional submanifolds. A general method is given which applies whenever the fundamental solution to the principal part is an integrable measure. Particular cases are semilinear first order systems in one space variable and the semilinear Klein-Gordon equation in at most three space variables.     

HOMOGENIZATION OF SOME LINEAR AND SEMILINEAR SCHRDINGER EQUATIONS WITHREAL POTENTIAL

1 IntroductionIn this paPer, we collsider the initial and boundaxy value probIem of linear and sentilillearScl1r5dinger equation as fOllows:l ie(x):5:i".,'<">"'>.'<",,'>,"=' 1:!\:?0t:)t>, (l1)wllere E > 0, fl C RN is a bounded open dolllain and T is an ar…     

The problem of start control for a class of semilinear distributed systems of Sobolev type

A result on the solvability of the Cauchy problem for a semilinear equation of Sobolev type in a Banach space is obtained with the help of the theory of degenerate operator semigroups. The result is used for investigating the problem of start control in the corresponding system. Abstract results are illustrated by the example of the semilinear Dzektser equation.     

Global attractor for the semilinear thermoelastic problem

In this paper we consider a class of semilinear thermoelastic problems. The global attractor for this semilinear thermoelastic problem with Dirichlet boundary condition is obtained. Copyright © 2003 John Wiley & Sons, Ltd.