Abstract:We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional system of rst-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder xed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.
We study the classification schemes for nonoscillatory solutions of a class of nonlinear two dimensional systems of first order delay dynamic equations on time scales. Necessary and sufficient conditions are also given in order to show the existence and nonexistence of such solutions and some of our results are new for the discrete case. Examples will be given to illustrate some of our results.
In this article, we establish some new criteria for the oscillation of fourth-order nonlinear delay differential equations of the form (r2(t)(r1(t)(y (t)) α ) ) + p(t)(y (t)) α + q(t)f (y(g(t))) = 0 provided that the second-order equationis nonoscillatory or oscillatory.Mathematics Subject Classification. 34C10, 39A10.
In this paper, we generalize and compare Gompertz and Logistic dynamic equations in order to describe the growth patterns of bacteria and tumor. First of all, we introduce two types of Gompertz equations, where the first type 4-paramater and 3-parameter Gompertz curves do not include the logarithm of the number of individuals, and then we derive 4parameter and 3-parameter Logistic equations. We notice that Logistic curves are better in modeling bacteria whereas the growth pattern of tumor is described better by Gompertz curves. Increasing the number of parameters of Logistic curves give favorable results for bacteria while decreasing the number of parameters of Gompertz curves for tumor improves the curve fitting. Moreover, our results overshadow some of the existing results in the literature.
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