共查询到18条相似文献,搜索用时 15 毫秒
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利用上、下解方法讨论了抛物方程组解的存在唯一性,并证明了解关于耦合函数的连续依赖性,同时给出了误差估计. 相似文献
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《常微分方程》传统的教材均先证明Bellman引理,然后利用Bellman引理完成"解对初值连续依赖定理"的证明.本文用曲线平移的方法构造出比较函数,从而给出了解对初值连续依赖定理的一种新的且具有几何直观性的证明方法. 相似文献
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This paper mainly concerns with a class of nonlinear Hilfer fractional neutral recurrent neural networks with time varying delays. The existence and uniqueness of solutions in the space of weighted continuous functions are established by Banach''s contraction principle. Finally, an example is provided to illustrate the application of the obtained results. 相似文献
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具分段连续时滞的微分系统的周期解与稳定性 总被引:2,自引:1,他引:1
讨论了一类具分段连续时滞的高维微分系统的周期解的存在唯一性和全局渐近稳定性,得到了新的实用的判别条件,推广或改进了文[2-4,6,9]的相关结果.. 相似文献
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General boundary value problems are considered for general parabolic (in the Douglas–Nirenberg–Solonnikov sense) systems. The dependence of solution uniqueness classes of these problems on the geometry of a nonbounded domain is established. 相似文献
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利用Henstock积分,讨论了一类不连续系统有界变差解对参数的连续依赖性及其它相关性质. 相似文献
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Josef Malík 《Applications of Mathematics》1998,43(6):413-438
The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties. 相似文献
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Josef Malík 《Applications of Mathematics》2000,45(3):177-203
The main goal of the paper is to describe a reinforcement consisting of fully grouted bolts, which is applied to stabilizing underground openings and tunnels. After a variational formulation is given, the existence and uniqueness is proved. Some asymptotic results that make it possible to replace the real system with a continuous one more suitable for discretization are presented. Some other types of reinforcements and properties are studied. 相似文献
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文[6]讨论了比已有结果更弱的假设条件下,固定时刻一阶脉冲微分系统与Kurzweil广义常微.分方程的关系,本文在此基础之上,建立了此类脉冲微分系统有界变差解对参数的连续依赖性定理. 相似文献
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讨论了一类三次系统x=-y(1-βx2)-(a1x a2x2 a3x3),y=b1x b2x2 b3x3的极限环问题.对包含一个奇点或多个奇点的极限环的唯一性和唯二性给出了若干充分条件. 相似文献
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Phan Quoc Khanh 《Numerical Functional Analysis & Optimization》2018,39(1):100-125
We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations. 相似文献
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利用基于集合Ph,e上的一类混合单调算子不动点定理,研究了一类Riemann Liouville分数阶微分方程两点边值问题,获得了这类方程在集合Ph,e中解的存在性与唯一性,并用一组单调迭代序列逼近了该方程的唯一非平凡解.最后,利用一个实例验证了主要结论. 相似文献
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邱镜亮 《数学的实践与认识》2017,(10):262-269
应用锥不动点定理并结合Banach空间中的半序结构,研究了一类梁方程的可解性问题.不仅得到了梁方程正解的存在性结果,并且讨论了梁方程正解对参数的依赖性.注意到梁方程中含有正参数λ和L~p-可积函数,获得的结果是新的,并从本质上推广了已有文献的结果. 相似文献
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Stanislav Sysala 《Applications of Mathematics》2008,53(4):347-379
The mathematical model of a beam on a unilateral elastic subsoil of Winkler’s type and with free ends is considered. Such
a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are
formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases
for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated
by the finite element method and the relation between the original problem and the family of approximated problems is analyzed.
The error estimates are derived in dependence on the smoothness of the solution, the load and the discretization parameter
of the partition.
This work was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AVOZ 30860518. 相似文献
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Mark Lichtner Mindaugas Radziunas Lutz Recke 《Mathematical Methods in the Applied Sciences》2007,30(8):931-960
We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献