共查询到20条相似文献,搜索用时 78 毫秒
1.
Zhaoli Liu 《数学学报(英文版)》2000,16(3):505-514
Abstract
This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations.
We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a priori bound we prove the existence of at least one T-periodic solution under some general conditions
Research supported by the NNSF of China and the RFDP of China. 相似文献
2.
Ying Zhang 《Mathematical Methods in the Applied Sciences》2013,36(13):1734-1745
In this paper, we consider the global existence of weak solutions for a two‐component μ‐Camassa–Holm system in the periodic setting. Global existence for strong solutions to the system with smooth approximate initial value is derived. Then, we show that the limit of approximate solutions is a global‐in‐time weak solution of the two‐component μ‐Camassa–Holm system. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
3.
Zhenjie Liu 《分析论及其应用》2009,25(4):369-380
This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis
functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence
degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time
scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method
is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference
equations. 相似文献
4.
This article is concerned with a stochastic model of gene expression with distributed delay and degenerate diffusion. We transform the model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is of degenerate type, the uniform ellipticity condition is not satisfied. The Markov semigroup theory is used to obtain the existence and uniqueness of a stable stationary distribution. We prove the densities of the distributions of the solutions can converge in L1 to an invariant density. The existence of the stationary distribution implies stochastic weak stability. Numerical simulation is introduced to illustrate the analytical result. 相似文献
5.
Xing-Bin Pan 《Calculus of Variations and Partial Differential Equations》2009,36(3):317-342
This paper concerns a quasilinear system involving the operator curl. This system is an approximation of the anisotropic Ginzburg–Landau
system which describes the Meissner state of type II superconductors. The existence of the weak solutions of the quasilinear
system is proved by applying a variational method to a modified functional, and the C
2+α
regularity of the weak solutions H is established without assuming the boundedness of curl H. 相似文献
6.
Global bifurcation of positive solutions for some degenerate quasilinear elliptic problems is considered. The uniform estimate
of the gradient of weak solutions is given. This estimate is crucial in our arguments.
Received: 10 August 2001
Supported in part by Grant-in-Aid for Scientific Research (No. 11640207), Ministry of Education, Science, Sports and Culture,
Japan.
Mathematics Subject Classification (2000): 35B32, 35J25, 35J70 相似文献
7.
F. Cammaroto 《Numerical Functional Analysis & Optimization》2014,35(7-9):911-931
In this article, we establish the existence of three weak solutions for a nonlinear transmission problem involving degenerate nonlocal coefficients of p(x)–Kirchhoff–type. Our approach is of variational nature; the weak formulation takes place in suitable variable exponent Sobolev spaces. 相似文献
8.
This paper is concerned with global existence of weak solutions for a periodic two-component?μ-Hunter–Saxton system. We first derive global existence for strong solutions to the system with smooth approximate initial data. Then, we show that the limit of approximate solutions is a global weak solution of the two-component?μ-Hunter–Saxton system. 相似文献
9.
Anna Lisa Amadori 《Ricerche di matematica》2007,56(1):1-17
Abstract We study the obstacle problem for a class of nonlinear integro-partial differential equations of second order, possibly degenerate,
which includes the equation modeling American options in a jump-diffusion market with large investor. The viscosity solutions
setting reveals appropriate, because of a monotonicity property with respect to the integral term. The same property allows
to approximate the problem by penalization and to obtain the existence and uniqueness of solutions via a comparison principle.
We also give uniform estimates of the solutions of the penalized problems which allow to prove further regularity.
Keywords: Integro-differential equations, Obstacle problem, Viscosity solutions, American options
Mathematics Subject Classification (2000): 45K05, 35K85, 49L25, 91B24 相似文献
10.
M. Bostan 《Mathematical Methods in the Applied Sciences》2006,29(15):1801-1848
In this work, we study the existence of time periodic weak solution for the N‐dimensional Vlasov–Poisson system with boundary conditions. We start by constructing time periodic solutions with compact support in momentum and bounded electric field for a regularized system. Then, the a priori estimates follow by computations involving the conservation laws of mass, momentum and energy. One of the key point is to impose a geometric hypothesis on the domain: we suppose that its boundary is strictly star‐shaped with respect to some point of the domain. These results apply for both classical or relativistic case and for systems with several species of particles. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
11.
The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang, T., Zhu, C. J.: Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum II. J. Differential Equations, 192(2), 475-501 (2003)]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → +∞ for any θ 〉 0 is also given. 相似文献
12.
原保全 《数学物理学报(A辑)》2008,28(4):627-635
该文用单模方法在Lorentz空间研究了抛物椭圆方程组奇异解和正则解的存在性, 其中初值属于Lorentz空间Ln/2,∞ (Rn), n≥ 3. 利用时间加权的Lorentz空间, 还得到了其正则解. 此外, 如果初值满足自相似结构, 也得到了自相似解的存在性. 相似文献
13.
In this paper, we study discontinuous solutions of a partial differential equation of strongly degenerate parabolic type. A notion of weak solutions of BV class is proposed, and existence and uniqueness results are obtained. 相似文献
14.
The periodic solution bifurcated from homoclinic orbit for coupled ordinary differential equations 下载免费PDF全文
We consider the problem of the periodic solutions bifurcated from a homoclinic orbit for a pair of coupled ordinary differential equations in . Assume that the autonomous system has a degenerate homoclinic solution γ in . A functional analytic approach is used to consider the existence of periodic solution for the autonomous system with periodic perturbations. By exponential dichotomies and the method of Lyapunov–Schmidt, the bifurcation function defined between two finite dimensional subspaces is obtained, where the zeros correspond to the existence of periodic solutions for the coupled ordinary differential equations near . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
15.
Blanca Climent-Ezquerra Francisco Guillén-González Marko Rojas-Medar 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):984-998
In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE’s system related
to a nematic liquid crystal model.
This problem is relatively explict when time-independent Dirichlet boundary conditions are imposed for the orientation of
crystal molecules. Nevertheless, for the time-dependent case, the treatment of the problem is completely different. The verification
of a maximum principle for weak reproductive solutions is fundamental in the argument.
Finally, the relation between reproductive and periodic in time (regular) solutions will be pointed out, differenting the
2D and 3D cases. Basically, in two-dimensional domains every reproductive solution is regular and time periodic, whereas the problem
remains open for three-dimensional domains. 相似文献
16.
Yong Xiang LI 《数学学报(英文版)》2005,21(3):491-496
In this paper the existence results of oscillatory periodic solutions are obtained for a second order ordinary differential equation -u″(t) = f(t, u(t)), where f : R^2 → R is a continuous odd function and is 2π-periodic in t. The discussion is based on the fixed point index theory in cones. 相似文献
17.
We prove existence and uniqueness results for weak solutions of
nonlinear degenerate problems arising in various physical models. The main
novelty in the article concerns the uniqueness, which employs a technique
based in showing that weak solutions are also entropy solutions, for which
uniqueness follows from a straightforward adaptation of known results. We
treat equations with lower order terms that have a particular structure and
show with a counterexample that for general lower order terms the uniqueness
does not hold.AMS Subject Classification: 35D99, 35K65, 35R35. 相似文献
18.
19.
Takahiro Okabe 《Journal of Evolution Equations》2011,11(2):265-286
We consider the initial boundary value problem to the Navier–Stokes equations in a bounded domain with the inhomogeneous time-dependent
data b(t) ? H1/2(?W){\beta(t) \in H^{1/2}(\partial\Omega)} under the general flux condition. We establish a reproductive property for weak solutions of the Navier–Stokes equations.
Here, the reproductive property is regarded as the generalization of the time periodicity. As an application, we can prove
the existence of periodic weak solutions. 相似文献
20.
For an arbitrary domain Ω ⊂ ℝn, n=2,3, Ω ≠ ℝn, we prove the existence of weak periodic solutions to the Navier-Stokes equations and of regular solutions if the data are
small or satisfy certain symmetry conditions. We also show that the periodic regular solutions are stable. Bibliography: 38
titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1996, pp. 142–182. 相似文献