For a second order differential equation with a damping term, we establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivative. We also obtain a lower bound for the first eigenvalue of a boundary value problem. The main results are proved by applying the Hölder inequality and some generalizations of Opial and Wirtinger type...

We give criteria for domination of strongly continuous semigroups in ordered Banach spaces that are not necessarily lattices, and thus obtain generalizations of certain results known in the lattice case. We give applications to semigroups generated by differential operators in function spaces which are not lattices.

While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...

While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...

In this paper, by applying a simple mathematical model imitating the equation of state, behaviour of the phase transition curve near the critical point is investigated. The problem of finding the unique vapour-liquid equilibrium curve passing through the critical point is reduced to solving a nonlinear system of differential equations.

Digestion in the small intestine is the result of complex mechanical and biological phenomena which can be modelled at different scales. In a previous article, we introduced a system of ordinary differential equations for describing the transport and degradation-absorption processes during the digestion. The present article sustains this simplified model by showing that it can be seen as a macroscopic version of more realistic models including biological phenomena at lower scales. In other words,...

In this paper, we propose a mathematical model for flow and transport processes of diluted solutions in domains separated by a leaky semipermeable membrane. We formulate transmission conditions for the flow and the solute concentration across the membrane which take into account the property of the membrane to partly reject the solute, the accumulation of rejected solute at the membrane, and the influence of the solute concentration on the volume flow, known as osmotic effect. The model is solved...

This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which...

The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties of leukemic stem cells to those of their benign counterparts....

Recent discovery of cancer stem cells in tumorigenic tissues has raised many questions about their nature, origin, function and their behavior in cell culture. Most of current experiments reporting a dynamics of cancer stem cell populations in culture show the eventual stability of the percentages of these cell populations in the whole population of cancer cells, independently of the starting conditions. In this paper we propose a mathematical model...

We consider limit cycles of a class of polynomial differential systems of the form $$\left\{\begin{array}{c}\dot{x}=y,\hfill \\ \dot{y}=-x-\epsilon (g_{21}\left(x\right)y^{2\alpha +1}+f_{21}\left(x\right)y^{2\beta })-{\epsilon }^2(g_{22}\left(x\right)y^{2\alpha +1}+f_{22}\left(x\right)y^{2\beta }),\hfill \end{array}\right.$$ where $\beta$ and $\alpha$ are positive integers, $g_{2j}$ and $f_{2j}$ have degree $m$ and $n$, respectively, for each $j=1,2$, and $\epsilon$ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot{x}=y$, $\dot{y}=-x$ using the averaging theory of first and second order.