• Title, Summary, Keyword: coincidence degree theory

Search Result 11, Processing Time 0.026 seconds

THE EXISTENCE OF PERIODIC SOLUTION OF A TWO-PATCHES PREDATOR-PREY DISPERSION DELAY MODELS WITH FUNCTIONAL RESPONSE

  • Zhang, Zhengqiu;Wang, Zhicheng
    • Journal of the Korean Mathematical Society
    • /
    • v.40 no.5
    • /
    • pp.869-881
    • /
    • 2003
  • In this paper, a nonautonomous predator-prey dispersion delay models with functional response is studied. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for above models is established.

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A KIND OF RAYLEIGH EQUATION WITH A DEVIATING ARGUMENT

  • Zhou, Qiyuan;Xiao, Bing;Yu, Yuehua;Liu, Bingwen;Huang, Lihong
    • Journal of the Korean Mathematical Society
    • /
    • v.44 no.3
    • /
    • pp.673-682
    • /
    • 2007
  • In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for a kind of Rayleigh equation with a deviating argument of the form $x'+f(x'(t))+g(t,\;x(t-\tau(t)))=p(t)$.

PERIODIC SOLUTIONS FOR DUFFING TYPE p-LAPLACIAN EQUATION WITH MULTIPLE DEVIATING ARGUMENTS

  • Jiang, Ani
    • Journal of applied mathematics & informatics
    • /
    • v.31 no.1_2
    • /
    • pp.27-34
    • /
    • 2013
  • In this paper, we consider the Duffing type p-Laplacian equation with multiple deviating arguments of the form $$({\varphi}_p(x^{\prime}(t)))^{\prime}+Cx^{\prime}(t)+go(t,x(t))+\sum_{k=1}^ngk(t,x(t-{\tau}_k(t)))=e(t)$$. By using the coincidence degree theory, we establish new results on the existence and uniqueness of periodic solutions for the above equation. Moreover, an example is given to illustrate the effectiveness of our results.

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF A PERIODIC SOLUTION TO DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS

  • Zhang, Zhengqiu;Wang, Liping
    • Journal of the Korean Mathematical Society
    • /
    • v.48 no.4
    • /
    • pp.727-747
    • /
    • 2011
  • By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

NEW CONDITIONS ON EXISTENCE AND GLOBAL ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS FOR BAM NEURAL NETWORKS WITH TIME-VARYING DELAYS

  • Zhang, Zhengqiu;Zhou, Zheng
    • Journal of the Korean Mathematical Society
    • /
    • v.48 no.2
    • /
    • pp.223-240
    • /
    • 2011
  • In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OF p-LAPLACIAN EQUATIONS

  • Kim, Yong-In
    • The Pure and Applied Mathematics
    • /
    • v.19 no.2
    • /
    • pp.103-109
    • /
    • 2012
  • The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: $$({\phi}_p(x^{\prime}))^{\prime}+{\alpha}(t)x^{\prime}+g(t,x)=e(t),\;x(0)=x(T),x^{\prime}(0)=x^{\prime}(T)$$ are investigated, where ${\phi}_p(u)={\mid}u{\mid}^{p-2}u$ with $p$ > 1 and ${\alpha}{\in}C^1$, $e{\in}C$ are T-periodic and $g$ is continuous and T-periodic in $t$. By using coincidence degree theory, some existence and uniqueness results are obtained.

SOLVABILITY FOR SECOND-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS ON AN UNBOUNDED DOMAIN AT RESONANCE

  • Yang, Ai-Jun;Wang, Lisheng;Ge, Weigao
    • The Pure and Applied Mathematics
    • /
    • v.17 no.1
    • /
    • pp.39-49
    • /
    • 2010
  • This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$ where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.