共查询到20条相似文献,搜索用时 140 毫秒
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本文利用Rellich恒等式建立了Heisenberg群上一类半线性方程解的非存在性结果. 相似文献
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本文建立了Heisenberg型群G上的一些积分恒等式 ,得到了G上半线性次Laplace方程非负解的一个不存在性定理 相似文献
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本文研究了关于Heisenberg群上的广义Morrey空间和Carnot群上的Lebesgue空间中Riesz位势算子或者分数阶极大算子的行为.根据Heisenberg群中抽象调和分析方法以及sub Laplacian算子的Dirichlet问题解的表示公式,本文主要给出了关于齐次Carnot群G上消失的广义Morrey空间V L~(p,?)(G)中的加权Hardy算子、分数阶极大算子和分数阶位势算子的有界性刻画.进而也得到无消失模的广义Morrey空间上Morrey位势的浸入不等式.所有这些结果推广了关于Heisenberg群上的广义Morrey空间和Carnot群上的Lebesgue空间中的相关结论. 相似文献
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本文建立一个新的非线性Picone恒等式,它包括一些已有的Picone恒等式.利用这个新的Picone恒等式,我们给出了带奇异项p-Laplace方程的Sturm比较原理,p-Laplace方程组的Liouville定理和带权Hardy不等式.由这里一般的带权Hardy型不等式,我们可以得到几个新的有趣的带权型Hardy不等式. 相似文献
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利用一些非常精细的估计技巧,证明了各向异性Heisenberg群上的一类带余项的Hardy型不等式,推广了最近文献中关于Heisenberg群上的带余项的Hardy型不等式的结果. 相似文献
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崔尚斌 《数学年刊A辑(中文版)》1991,(6)
本文通过引进可控型左不变算子的概念,讨论了Heisenberg群上非齐次左不变LPDO的局部可解性,得到了一些关于这类算子局部可解的充要条件。 相似文献
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Zhi-Han Zhao Yong-Kui Chang Juan J. Nieto 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1886-1894
In this paper we prove some existence results for almost automorphic and pseudo-almost automorphic mild solutions to a class of abstract differential equations in Banach spaces. The main technique is based on some composition theorems combined with the contraction mapping theorem. Finally, we present an application to a semilinear partial differential equation with Dirichlet conditions. 相似文献
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Mean Value Theorem and Pohozaev Type Identities of Generalized Greiner Operator and Their Applications
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In this paper, a fundamental solution at the origin and mean value theorem of generalized Greiner operator are given. Then the Hardy type inequality and some Pohozaev type identities are proved. As their applications, some nonexistence results of semilinear nonelliptic equation and unique continuation are discussed. 相似文献
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In this paper, we discuss the partial differential equation of Riccati type that describes the optimal filtering error covariance function for a linear distributed-parameter system with pointwise observations. Since this equation contains the Dirac delta function, it is impossible to apply directly the usual methods of functional analysis to prove existence and uniqueness of a bounded solution. By using properties of the fundamental solution and the classical technique of successive approximation, we prove the existence and uniqueness theorem. We then prove the comparison theorem for partial differential equations of Riccati type. Finally, we consider some applications of these theorems to the distributed-parameter optimal sensor location problem. 相似文献
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The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has an algebraically closed field of constants. In this paper, we prove the existence of a Picard-Vessiot extension for a homogeneous linear differential equation defined over a real differential field K with real closed field of constants. We give an adequate definition of the differential Galois group of a Picard-Vessiot extension of a real differential field with real closed field of constants and we prove a Galois correspondence theorem for such a Picard-Vessiot extension. 相似文献
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We consider a semilinear elliptic partial differential equation, depending on two positive parameters and , coupled with homogeneous Dirichlet boundary conditions. Assuming only one-sided growth conditions on the nonlinearities involved, we prove the existence of at least three weak solutions for and lying in convenient intervals. We employ techniques of nonsmooth analysis introduced by Degiovanni and Zani, and a theorem of Ricceri for multiplicity of local minimizers. 相似文献
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M. V. Bartuccelli 《Mathematical Methods in the Applied Sciences》2002,25(8):701-708
The objective of this paper aims to prove positivity of solutions for a semilinear dissipative partial differential equation with non‐linear diffusion. The equation is a generalized model of the well‐known Fisher–Kolmogorov equation and represents a class of dissipative partial differential equations containing differential operators of higher order than the Laplacian. It arises in a variety of meaningful physical situations including gas flows, diffusion of an electron–ion plasma and the dynamics of biological populations whose mobility is density dependent. In all these situations, the solutions of the equation must be positive functions. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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Xu Yancong Zhu Deming 《Annals of Differential Equations》2008,(4):457-469
Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references. 相似文献
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《Optimization》2012,61(5):1017-1035
ABSTRACTThe purpose of this paper is to study a class of semilinear differential variational systems with nonlocal boundary conditions, which are obtained by mixing semilinear evolution equations and generalized variational inequalities. First we prove essential properties of the solution set for generalized variational inequalities. Then without requiring any compactness condition for the evolution operator or for the nonlinear term, two existence results for mild solutions are established by applying a weak topology technique combined with a fixed point theorem. 相似文献
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We study a forward-backward system
of stochastic differential equations in an
infinite-dimensional framework and its relationships
with a semilinear parabolic differential equation on a Hilbert space,
in the spirit of the approach of Pardoux-Peng.
We prove that the stochastic system
allows us to construct a unique
solution of the parabolic equation in
a suitable class of locally Lipschitz real
functions. The parabolic equation is understood in
a mild sense which requires the notion
of a generalized directional gradient, that
we introduce by a probabilistic approach
and prove to exist for locally Lipschitz
functions.
The use of the generalized directional gradient
allows us to cover various applications to option
pricing problems and to optimal stochastic control problems
(including control of delay equations and
reaction--diffusion equations),
where the lack of differentiability of the coefficients
precludes differentiability of solutions to the associated
parabolic equations of Black--Scholes or Hamilton-Jacobi-Bellman
type. 相似文献
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《随机分析与应用》2013,31(2):403-427
Abstract In this paper, we set up the comparison theorem between the mild solution of semilinear time-delay stochastic evolution equation with general time-delay variable and the solution of a class (1-dimension) deterministic functional differential equation, by using the Razumikhin–Lyapunov type functional and the theory of functional differential inequalities. By applying this comparison theorem, we give various types of the stability comparison criteria for the semilinear time-delay stochastic evolution equations. With the aid of these comparison criteria, one can reduce the stability analysis of semilinear time-delay stochastic evolution equations in Hilbert space to that of a class (1-dimension) deterministic functional differential equations. Furthermore, these comparison criteria in special case have been applied to derive sufficient conditions for various stability of the mild solution of semilinear time-delay stochastic evolution equations. Finally, the theories are illustrated with some examples. 相似文献