Comparison Theorems for first Order Nonlinear Functional Differebtial Equations
In this paper the oscillatory and asymptotic properties of the solutions of the functional differential equation are compared with those of the functional differential equation .
The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.
In this paper we study asymptotic properties of the third order trinomial delay differential equation by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.
Complementary analysis of a model of the human immune system after a series of vaccinations, proposed in [7] and studied in [6], is presented. It is shown that all coordinates of every solution have at most two extremal values. The theoretical results are compared with experimental data.
We show that the half-linear differential equation with -periodic positive functions is conditionally oscillatory, i.e., there exists a constant such that () with instead of is oscillatory for and nonoscillatory for .
A sufficient integral condition for the absence of eventually positive solutions of a first order stable type differential inequality with one nondecreasing retarded argument is given. In the special case of equality the result becomes an oscillation criterion.