[Luo, ZG] Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
We apply the Krasnoselskii's fixed point theorem to study the existence of multiple positive periodic solutions for a class of impulsive functional differential equations with infinite delay and two parameters. In particular, the presented criteria improve and generalize some related results in the literature. As an application, we study some special cases of systems, which have been studied extensively in the literature.
By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t) = x(t)[a(t) - f(t,x(t), x(t - tau(1)(t, x(t))), ... , x(t - tau(n)(t, x(t))), x'(t - gamma(1)(t,x(t))), ... , x'(t - gamma(m)(t, x(t))))], t not equal t(k), k subset of Z(+); x(t(k)(+)) = x(t(k)(-)) + theta(k)(x(t(k))), k subset of Z(+). As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.
We investigate a neutral multispecies logarithmic population model with feedback control and impulse. By applying the contraction mapping principle and some inequality techniques, a set of easily applicable criteria for the existence, uniqueness, and global attractivity of positive periodic solution are established. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases. We also give an example to illustrate the applicability of our results.
[LUO Liping] Department of Mathematics, Hengyang Normal University
impulse;quasilinear;delay;system of hyperbolic equations;oscillation
In this paper, oscillatory properties for solutions of the systems of certain quasilinear impulsive delay hyperbolic equations with nonlinear diffusion coefficient are investigated. A sufficient criterion for oscillations of such systems is obtained.
Chinese Quarterly Journal of Mathematics,2008年23(01):67-74 ISSN：1002-0462
[罗李平] Department of Mathematics,Hengyang Normal University
nonlinear;neutral;partial;nonlinear;neutral;partial differential equation;oscillation;continuous distribution delay
In this paper,some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet's boundary value conditions.