共查询到20条相似文献，搜索用时 31 毫秒
1.
This paper is concerned with the traveling wave solutions in a diffusive system with two preys and one predator. By constructing upper and lower solutions, the existence of nontrivial traveling wave solutions is established. The asymptotic behavior of traveling wave solutions is also confirmed by combining the asymptotic spreading with the contracting rectangles. Applying the theory of asymptotic spreading, the nonexistence of traveling wave solutions is proved. 相似文献
2.
Xinjian Wang 《Applicable analysis》2013,92(14):2619-2638
This paper is concerned with the time periodic traveling wave solutions for a periodic Lotka–Volterra predator–prey system, which formulates that both species synchronously invade a new habitat. We first establish the existence of periodic traveling wave solutions by combining the upper and lower solutions with contracting mapping principle and Schauder’s fixed point theorem. The asymptotic behavior of nontrivial solution is given precisely by the stability of the corresponding kinetic system that has been widely investigated. Then, the nonexistence of periodic traveling wave solutions is confirmed by applying the theory of asymptotic spreading. We show the conclusion for all positive wave speed and obtain the minimal wave speed. 相似文献
3.
This article studies the existence of traveling wave solutions in
an integrodifference equation with weak compactness. Because of the special
kernel function that may depend on the Dirac function, traveling wave maps
have lower regularity such that it is difficult to directly look for a traveling wave
solution in the uniformly continuous and bounded functional space. In this
paper, by introducing a proper set of potential wave profiles, we can obtain
the existence and precise asymptotic behavior of nontrivial traveling wave
solutions, during which we do not require the monotonicity of this model. 相似文献
4.
《Journal of Difference Equations and Applications》2012,18(12):1680-1705
ABSTRACTThis paper deals with the propagation thresholds of competitive integrodifference systems, which may be non-monotone even if the interspecific competition vanishes. The purpose is to establish the propagation thresholds that two competitors invade a new habitat. We first obtain the minimal wave speed by presenting the existence and non-existence of non-trivial travelling wave solutions. Then we confirm the minimal wave speed is the spreading speed of one competitor if the initial condition admits non-empty compact support. 相似文献
5.
The traveling wave solutions connecting two equilibria for a delayed Logistic equation in a cylinder are obtained for any delay . We attain our goal by using the approach based on the combination of Schauder fixed point theory and the weak coupled upper–lower solutions method. Moreover, we prove that there is a constant that serves as the minimal wave speed of such traveling wave solutions. 相似文献
6.
This paper is concerned with the travelling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion–coexistence process of two competitors with age structure. The existence of non-trivial travelling wave solutions is obtained by constructing generalized upper and lower solutions. The asymptotic and non-existence of travelling wave solutions are proved by combining the theory of asymptotic spreading with the idea of contracting rectangle. 相似文献
7.
Luping Li Shugui Kang Lili Kong Huiqin Chen 《Journal of Difference Equations and Applications》2018,24(6):941-954
In this paper, we study the minimal wave speed of a competitive system. By constructing upper and lower solutions, we confirm the existence of travelling wave solution at the critical wave speed. This completes earlier results found in the literature. Our conclusion implies that the asymptotic decay behaviour of solutions at the critical wave speed is different from that of solutions at larger wave speeds. 相似文献
8.
The purpose of this paper is to investigate the stability and asymptotic behav-ior of the time-dependent solutions to a linear parabolic equation with nonlinear boundarycondition in relation to their corresponding steady state solutions. Then, the above resultsare extended to a semilinear parabolic equation with nonlinear boundary condition by an-alyzing the corresponding eigenvalue problem and using the method of upper and lowersolutions. 相似文献
9.
Yanling Meng Weiguo Zhang Shengqiang Zhang 《Journal of Applied Analysis & Computation》2019,9(5):1769-1800
The paper is concerned with the existence and qualitative features of entire solutions for delayed reaction diffusion monostable systems. Here the entire solutions mean solutions defined on the $ (x,t)inmathbb{R}^{N+1} $. We first establish the comparison principles, construct appropriate upper and lower solutions and some upper estimates for the systems with quasimonotone nonlinearities. Then, some new types of entire solutions are constructed by mixing any finite number of traveling wave fronts with different speeds $ cgeq c_* $ and propagation directions and a spatially independent solution, where $c_*>0$ is the critical wave speed. Furthermore, various qualitative properties of entire solutions are investigated. In particularly, the relationship between the entire solution, the traveling wave fronts and a spatially independent solution are considered, respectively. At last, for the nonquasimonotone nonlinearity case, some new types of entire solutions are also investigated by introducing two auxiliary quasimonotone controlled systems and establishing some comparison theorems for Cauchy problems of the three systems. 相似文献
10.
Li Zhang 《Journal of Difference Equations and Applications》2019,25(4):504-515
This paper is concerned with the existence of nontrivial entire solutions of integrodifference equations. By constructing proper auxiliary integrodifference equations and functions, we present the existence of nontrivial entire solutions even if the birth function is not monotone, which are different from the well-studied travelling wave solutions. The convergence of entire solutions is also given. 相似文献
11.
In this paper, we derive the existence of forced waves for diffusive competition systems in shifting environments. First, we derive two different classes of forced waves for a 3-species competition system. Then we obtain forced waves for 2-species competition systems with at least one weak competitor. In all cases, the minimal environmental shifting speeds are determined under the equal diffusivities condition. 相似文献
12.
This paper is concerned with the propagation modes of a second order integrodifference equation without monotonicity. The equation cannot generate monotone semifolws. By constructing auxiliary functions/equations and applying some known results, the minimal wave speed of traveling wave solutions and asymptotic speeds of spread are established. 相似文献
13.
In this paper, we extend the population genetics model of Weinberger(1978, Asymptotic behavior of a model in population genetics.Nonlinear Partial Differential Equations and Applications (J.Chadam ed.). Lecture Notes in Mathematics, vol. 648. New York:Springer, pp. 47–98.) to the case where a fraction ofthe population does not migrate after the selection process.Mathematically, we study the asymptotic behaviour of solutionsto the recursion un+1 = Qg[un], where
In the above definition of Qg, K is a probabilitydensity function and f behaves qualitatively like the Beverton–Holtfunction. Under some appropriate conditions on K and f, we showthat for each unit vector Rd, there exists a c*g() which hasan explicit formula and is the spreading speed of Qg in thedirection . We also show that for each c c*g(), there existsa travelling wave solution in the direction which is continuousif gf '(0) 1. 相似文献
14.
利用一个新的比较定理和乘积空间的锥理论,得出了Banach空间中的一般高阶积分—微分初值问题的解存在性. 相似文献
15.
Guo Lin Wan-Tong Li Shuxia Pan 《Journal of Difference Equations and Applications》2013,19(12):1429-1446
This paper is concerned with the travelling wavefronts of delayed lattice dynamical systems with global interaction. We establish the existence of the travelling wavefronts by upper–lower solutions technique and Schauder's fixed point theorem when the system satisfies the quasimonotone condition. The nonexistence of the travelling wavefronts of the system is considered by the comparison principle and the corresponding results of the scalar equation. Finally, we apply our main results to the Logistic model and Belousov–Zhabotinskii system on lattice. Our main finding here is that the global interaction can increase the minimal wave speed while the delay can decrease it. 相似文献
16.
考虑一类退化与非退化的稳态扩散模型。利用上、正解方法与Schauder不动点原理,证明此类稳态扩散模型在一定条件下正解的存在性。 相似文献
17.
This paper considers the travelling wave fronts to a delayed lattice differential equation.The existence of the travelling wave solutions is proved by making use of the technique of the upper and lower solutions developed by J Wu and X Zou in[6].This work extends that of [4]in a general class of nonlinear terms. 相似文献
18.
This paper is concerned with the existence, asymptotic behavior, strict monotonicity, and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed lattice competitive system. We first prove the existence of traveling wave fronts by constructing upper and lower solutions and Schauder’s fixed point theorem, and then, for sufficiently small intraspecific competitive delays, prove that these traveling wave fronts decay exponentially at both infinities. Furthermore, for system without intraspecific competitive delays, the strict monotonicity and uniqueness of traveling wave fronts are established by means of the sliding method. In addition, we give the exact decay rate of the stronger competitor under some technique conditions by appealing to uniqueness. 相似文献
19.
Convergence of Monotone Iterations for Differential Problem 总被引：4，自引：0，他引：4
Tadeusz Jankowski 《数学学报(英文版)》2000,16(4):711-720
We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter.
Existence of extremal solutions to such problems is proved.
Received April 15, 1999, Revised December 6, 1999, Accepted July 18, 2000 相似文献
20.
Canrong Tian 《Mathematical Methods in the Applied Sciences》2013,36(13):1713-1725
This paper is concerned with the existence, uniqueness, and asymptotic behavior of solutions for the quasilinear parabolic systems with mixed quasimonotone reaction functions, the elliptic operators in which are allowed to be degenerate. By the method of the coupled upper and lower solutions, and its monotone iterations, it shows that a pair of coupled upper and lower solutions ensures that the unique positive solution exists and globally stable if the quasisolutions are equal. Moreover, we study the asymptotic behavior of solutions to the Lotka–Volterra model with the density‐dependent diffusion. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献