共查询到20条相似文献,搜索用时 140 毫秒
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D.E.Leach[3]证明了下述定理:证明了一个同胚定理,利用它证明了方x"+g(x)=e(t)的一个2π周期解的存在性和唯一性定理.所证明的定理是上述定理的一个推广. 相似文献
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陈志国 《数学年刊A辑(中文版)》2000,(6)
本文研究μ(z)-同胚的紧致性.当一族μ(z)-同胚的伸张函数同时受控于一控制函数K(z)时,得到该族的紧致性质.利用紧性,得出一列μn(z)-同胚可收敛于一个拟共形映射.另外,还给出了μ(z)-同胚在其逆映射为ACL 情况下的分解定理. 相似文献
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王中生 《纯粹数学与应用数学》1993,9(2):21-24
由于实际的需要,人们对高维晨自治系统周期解的存在性、唯一性及稳定性进行了许多探讨。本文“间矩阵稳定性”理论及空间周期解理论中的基本结论,把微分方程中的两个方向结合起来,讨论了方程x=A(t.x)x+g(t.x)的周期解的存在、唯一及稳定性问题,给出了生类新的判定条件,便于实际应用。 相似文献
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非线性微分方程零解的全局吸引性与包围高阶奇点的极限环的存在性 总被引:1,自引:0,他引:1
非线性微分方程零解的全局吸引性与包围高阶奇点的极限环的存在性王向荣,冯滨鲁,韩茂安(山东矿业学院数学系泰安271019)关键词:全局吸引性;极限环;存在性AMS(1991)主题分类:34C05.考虑系统假设h,F,g均连续且满足解的存在唯一性条件,且... 相似文献
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一类非线性积分偏微分方程初边值问题的整体解 总被引:6,自引:0,他引:6
郭艾 《数学物理学报(A辑)》1999,19(1):30-38
讨论初边值问题整体经典解的存在性.在P′(s)≥0,p′(s)─q′(s)|≤const.的条件下,用Galerkin方法证明了该问题整体经典解的存在唯一性. 相似文献
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本文利用构造上、下解方法,研究奇异方程、(t)X''=f(t,x)的极限边值问题解的存在唯一性,证明了Thoms-Fermi方程对应于孤立中性原子型边值问题有唯一解,所得结果推广了A.Mambriani定理 相似文献
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Zhanbing Bai 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):916-1725
In this paper, we investigate the existence and uniqueness of positive solutions for a nonlocal boundary value problem of fractional differential equation. Firstly, we give Green’s function and prove its positivity; secondly, the uniqueness of positive solution is obtained by the use of contraction map principle and some Lipschitz-type conditions; thirdly, by means of the fixed point index theory, we obtain some existence results of positive solution. The proofs are based upon the reduction of the problem considered to the equivalent Fredholm integral equation of second kind. 相似文献
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中立型泛函微分方程周期解问题 总被引:1,自引:0,他引:1
利用Fourier级数理论研究了一类k-阶线性中立型泛函微分方程周期解问题,给出了周期解存在唯一性的充要条件。利用此结果并结合Schauder不动点原理,进一步研究了一类k-阶非线性中立型泛函微分方程,得到了存在周期解的新的结果。这些结果改进和推广了近期文献中的已有结论。 相似文献
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Monotone iterative technique for neutral fractional differential equation with infinite delay 下载免费PDF全文
Renu Chaudhary Dwijendra N. Pandey 《Mathematical Methods in the Applied Sciences》2016,39(15):4642-4653
In this paper, we employ the method of lower and upper solutions coupled with the monotone iterative technique to obtain existence and uniqueness of extremal mild solutions to neutral fractional differential equation with infinite delay in an ordered Banach space. The results are obtained by using the theory of fractional calculus, monotone iterative technique, measure of noncompactness, and semigroup theory. Finally, we discuss an example to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Xiulin Hu Dept.of Math.and Physics Hefei University Hefei Zongfu Zhou 《Annals of Differential Equations》2012,(1):48-57
In this paper,using the principle of a priori boundedness,we study the existence and uniqueness of periodic solutions to a high-order neutral functional differential equation.Some new results for the existence and uniqueness of the periodic solution are obtained. 相似文献
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In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of upper and lower solutions and compactness and continuity conditions. The results in this paper are applied to a class of abstract semilinear evolution equations with noncompact semigroup in Banach spaces and the initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces. The results obtained here improve and generalize many known results. 相似文献
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Alessio Figalli 《Journal of Functional Analysis》2008,254(1):109-153
In this paper we extend recent results on the existence and uniqueness of solutions of ODEs with non-smooth vector fields to the case of martingale solutions, in the Stroock-Varadhan sense, of SDEs with non-smooth coefficients. In the first part we develop a general theory, which roughly speaking allows to deduce existence, uniqueness and stability of martingale solutions for Ld-almost every initial condition x whenever existence and uniqueness is known at the PDE level in the L∞-setting (and, conversely, if existence and uniqueness of martingale solutions is known for Ld-a.e. initial condition, then existence and uniqueness for the PDE holds). In the second part of the paper we consider situations where, on the one hand, no pointwise uniqueness result for the martingale problem is known and, on the other hand, well-posedness for the Fokker-Planck equation can be proved. Thus, the theory developed in the first part of the paper is applicable. In particular, we will study the Fokker-Planck equation in two somehow extreme situations: in the first one, assuming uniform ellipticity of the diffusion coefficients and Lipschitz regularity in time, we are able to prove existence and uniqueness in the L2-setting; in the second one we consider an additive noise and, assuming the drift b to have BV regularity and allowing the diffusion matrix a to be degenerate (also identically 0), we prove existence and uniqueness in the L∞-setting. Therefore, in these two situations, our theory yields existence, uniqueness and stability results for martingale solutions. 相似文献
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蒋玲芳 《纯粹数学与应用数学》2012,(2):256-261
讨论了一类非线性一阶常微分方程边值问题解的存在惟一性.得到了当参数在一定的范围取值时解存在惟一的充分条件,并包含了一些已知结果.主要结果基于Leray-Schauder非线性抉择理论和Banach不动点定理. 相似文献
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《Annals of Differential Equations》2012,(2):186-193
In this paper, based on the theory of (h, k)-Dichotomy of linear system and Kras-noselskii’s fixed point theorem, we study the existence of periodic solutions to a neutral differential equation. Some new sufficient conditions are obtained to guarantee the existence and uniqueness of T-periodic solution to the equation. 相似文献
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In this paper, we deal with a diffusive predator-prey model with mixed boundary conditions, in which the prey population can escape from the boundary of the domain while predator population can only live in this area and can not leave. We first investigate the asymptotic behaviour of positive solutions and obtain a necessary condition ensuring the existence of positive steady state solutions. Next, we investigate the existence of positive steady state solutions by using maximum principle, the fixed point index theory, Lpestimation, and embedding theorems, Finally, local stability and uniqueness are obtained by linear stability theory and perturbation theory of linear operators. 相似文献
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We study subdifferential initial boundary-value problems for the magneto-hydrodynamics (MHD) equations of a viscous incompressible liquid. We construct a solvability theory for an abstract evolution inequality in Hilbert space for operators with quadratic nonlinearity. The results obtained are applied to the study of MHD flows. For three-dimensional flows, we prove the existence of weak solutions of variational inequalities “globally” with respect to time, while, for two-dimensional flows, we establish the existence and uniqueness of strong solutions. 相似文献