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1.
In this paper, the competitor-competitor-mutualist three-species Lotka-Volterra model is discussed. Firstly, by Schauder fixed point theory, the coexistence state of the strongly coupled system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak. Secondly, the existence and asymptotic behavior of T-periodic solutions for the periodic reaction-diffusion system under homogeneous Dirichlet boundary conditions are investigated. Sufficient conditions which guarantee the existence of T-periodic solution are also obtained. 相似文献
2.
Tianwei Zhang Yongkun LiYuan Ye 《Communications in Nonlinear Science & Numerical Simulation》2012,17(3):1408-1422
In this paper, we consider an almost periodic Schoener’s competition model with delays and impulsive effects. Sufficient conditions which guarantee the permanence of the model and the existence of a unique uniformly asymptotically stable positive almost periodic solution are obtained. The result of this paper is completely new. An suitable example is employed to illustrate the feasibility of the main results. 相似文献
3.
This paper is concerned about a reaction-diffusion equation on n-dimensional isotropically growing domain, which describes the insect dispersal. The model for growing domains is first derived, and the comparison principle is then presented. The asymptotic behavior of the solution to the reaction-diffusion problem is given by constructing upper and lower solutions. Our results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution. Numerical simulations are also performed to illustrate the analytical results. 相似文献
4.
Chen Huang 《Journal of Mathematical Analysis and Applications》2022,505(2):125496
This paper considers the following general form of quasilinear elliptic equation with a small perturbation: where is a bounded domain with smooth boundary and small enough. We assume the main term in the equation to have a mountain pass structure but do not suppose any conditions for the perturbation term . Then we prove the equation possesses a positive solution, a negative solution and a sign-changing solution. Moreover, we are able to obtain the asymptotic behavior of these solutions as . 相似文献
5.
In this paper, a general reaction-diffusion food-limited population model with time-delay is proposed. Accordingly, the existence and uniqueness of the periodic solutions for the boundary value problem and the asymptotic periodicity of the initial-boundary value problem are considered. Finally, the effect of the time-delay on the asymptotic behavior of the solutions is given. 相似文献
6.
Fei Long 《Nonlinear Analysis: Real World Applications》2012,13(2):686-693
In this paper, we study the problem of positive almost periodic solutions for the generalized Nicholson’s blowflies model with a linear harvesting term and multiple time-varying delays. By applying the fixed point theorem and the Lyapunov functional method, we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results. 相似文献
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In this paper, the authors study the asymptotic behavior of solutions of second-order neutral type difference equations of the form
Δ2(yn+pyn−k)+f(n,yn−ℓ)=0,n