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1.
Existence of time periodic solutions for the 3-D viscous primitive equations of large-scale dry atmosphere 下载免费PDF全文
In this paper, we consider the existence of time periodic solutions of the 3-D viscous primitive equations of large-scale dry atmosphere. We used the Galerkin method. Firstly, by Leray-Schauder fixed point theorem, we prove the existence of approximate solutions of the primitive equations, then we show the convergence of the approximate solutions, and we also get the uniqueness to the primitive equations. 相似文献
2.
一类广义耦合的非线性波动方程组时间周期解的存在性 总被引:1,自引:1,他引:0
研究了一类广义耦合的非线性波动方程组关于时间周期解的问题.首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Laray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性. 相似文献
3.
We study the compressible Euler equation with an outer force. The global existence theorem has been proved in many papers, provided that the outer force is bounded. However, the stability of their solutions has not yet been obtained until now. Our goal in this paper is to prove the existence of a global solution without such an assumption as boundedness. Moreover, we deduce a uniformly bounded estimate with respect to the time. This yields the stability of the solution.When we prove the global existence, the most difficult point is to obtain the bounded estimate for approximate solutions. To overcome this, we employ an invariant region, which depends on both space and time variables. To use the invariant region, we introduce a modified difference scheme. To prove their convergence, we apply the compensated compactness framework. 相似文献
4.
Rafael Ortega 《Journal of Functional Analysis》2006,237(2):402-426
A celebrated result by Favard states that, for certain almost periodic linear differential systems, the existence of a bounded solution implies the existence of an almost periodic solution. A key assumption in this result is the separation among bounded solutions. Here we prove a theorem of anti-Favard type: if there are bounded solutions which are non-separated (in a strong sense) sometimes almost periodic solutions do not exist. Strongly non-separated solutions appear when the associated homogeneous system has homoclinic solutions. This point of view unifies two fascinating examples by Zhikov-Levitan and Johnson for the scalar case. Our construction uses the ideas of Zhikov-Levitan together with the theory of characters in topological groups. 相似文献
5.
讨论了时间标度上一类二阶非线性动态方程的周期边值问题正解以及多解的存在性,利用锥上的不动点理论给出了简捷的判别方法并举例。 相似文献
6.
Ying Yang Jingxue Yin Chunhua Jin 《Mathematical Methods in the Applied Sciences》2014,37(12):1736-1754
This paper is concerned with the existence and attractivity of time periodic solutions for one‐dimensional Nicholson's blowflies model with nonlinear diffusion. By constructing some suitable Lyapunov functionals and combining with Leray–Schauder fixed point theorem, we establish the existence of nonnegative time periodic solutions. Using the method of upper and lower solutions and its associated monotone iterations, we obtain the existence of the attractor for this model. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
7.
Rolf Reissig 《Annali di Matematica Pura ed Applicata》1970,85(1):235-240
Summary Applying the Leray-Schauder fixed point theorem we prove the existence of a periodic solution for a non-autonomous differential
equation with a bounded nonlinear term.
Entrata in Redazione il 18 agosto 1969. 相似文献
8.
Ying Yang Ran Zhang Chunhua Jin Jingxue Yin 《Mathematical Methods in the Applied Sciences》2010,33(7):922-934
This paper is concerned with the existence of periodic solutions of the Nicholson's blowflies model with Newtonian diffusion. By constructing some suitable Lyapunov functionals and combining with Leray–Schauder fixed point theorem, we establish the existence of nonnegative time periodic solutions. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
9.
Wenke Tan 《Journal of Functional Analysis》2011,261(5):1204-1226
In the paper, we first show the existence of global periodic conservative solutions to the Cauchy problem for a periodic modified two-component Camassa-Holm equation. Then we prove that these solutions, which depend continuously on the initial data, construct a semigroup. 相似文献
10.
Existence results for periodic solutions of integro-dynamic equations on time scales 总被引:1,自引:0,他引:1
Using the topological degree method and Schaefer’s fixed point theorem, we deduce the existence of periodic solutions of nonlinear
system of integro-dynamic equations on periodic time scales. Furthermore, we provide several applications to scalar equations,
in which we develop a time scale analog of Lyapunov’s direct method and prove an analog of Sobolev’s inequality on time scales
to arrive at a priori bound on all periodic solutions. Therefore, we improve and generalize the corresponding results in Burton
et al. (Ann Mat Pura Appl 161:271–283, 1992)
相似文献
11.
12.
In this paper we prove the existence of periodic solutions for gradient systems in finite and infinite dimensional spaces. The techniques of the proofs are based on the application of a global inverse functions theorem, the Schäefer fixed point theorem and the Faedou–Galerkin method. We apply our results in order to solve nonlinear reaction–diffusion equations with Dirichlet and Neumann boundary conditions. 相似文献
13.
This paper is concerned with the Nicholson blowflies equation with nonlinear diffusion and time delay subject to the homogeneous Dirichlet boundary condition in a bounded domain. We establish the existence of nontrivial periodic solutions of the time-periodic problem under general conditions by constructing a coupled upper–lower solution pair and by applying the Schauder fixed point theorem. The attractivity of the periodic solutions is also discussed by using the monotone iteration method. 相似文献
14.
《Mathematical Methods in the Applied Sciences》2018,41(10):3976-3997
A generalized non‐linear nonautonomous model for the haematopoiesis (cell production) with several delays and an oscillating circulation loss rate is studied. We prove a fixed point theorem in abstract cones, from which different results on existence and uniqueness of positive almost periodic solutions are deduced. Moreover, some criteria are given to guarantee that the obtained positive almost periodic solution is globally exponentially stable. 相似文献
15.
For abstract linear functional differential equations with a weighted pseudo-almost periodic forcing term, we prove that the existence of a bounded solution on R+ implies the existence of a weighted pseudo-almost periodic solution. Our results extend the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations. To illustrate the results, we consider the Lotka-Volterra model with diffusion. 相似文献
16.
This paper is concerned with a class of periodic degenerate parabolic system with time delays in a bounded domain under mixed boundary condition. Under locally Lipschitz condition on reaction functions, we apply Schauder fixed point theorem to obtain the existence of periodic solutions of the periodic problem. With quasi-monotonicity in addition, we also show that the periodic problem has a maximal and a minimal periodic solutions. Applications of the obtained results are also given to some nonlinear diffusion models arising from ecology. 相似文献
17.
Existence and exponential stability of unique almost periodic solution for Lasota–Wazewska red blood cell model with perturbation on time scales 下载免费PDF全文
Zhijian Yao 《Mathematical Methods in the Applied Sciences》2017,40(13):4709-4715
This paper deals with Lasota–Wazewska red blood cell model with perturbation on time scales. By applying the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence which converges to the almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by means of Gronwall inequality. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
18.
In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem. 相似文献
19.
Luca Biasco Jessica Elisa Massetti Michela Procesi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(3):711-758
In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain in [15] on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract “counter-term theorem” à la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find “many more” almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs. 相似文献
20.
Almost periodic solutions for neutral‐type neural networks with the delays in the leakage term on time scales 下载免费PDF全文
In this paper, a class of neutral‐type neural networks with delays in the leakage term on time scales are considered. By using the Banach fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solutions for this class of neural networks. The results of this paper are new and complementary to the previously known results. Finally, an example is presented to illustrate the effectiveness of our results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献