Lyapunov stability theory for dynamic systems on time scales.
Lyapunov type inequalities for a second order differential equation with a damping term
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...
Lyapunov type integral inequalities for certain differential equations.
Lyapunov-Razumikhin method for asymptotic stability of sets for impulsive functional differential equations.
Lyapunov-type inequality for higher-order differential equations
Majoration effective et application
Majorations affines du nombre de zéros d'intégrales abéliennes pour les hamiltoniens quartiques elliptiques
Majorization of -semigroups in ordered Banach spaces
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.
Mapping properties of regular and strongly degenerate elliptic differential operators in the Besov spaces . The case
Marachkov type stability results for functional differential equations.
Markov operators defined by Volterra type integrals with advanced argument
Markovian Master Equations. II.
Markovian master equations. III
Maslov index for homoclinic orbits of hamiltonian systems
Massive parallel implementation of ODE solvers
The presented contribution maps the possibilities of exploitation of the massive parallel computational hardware (namely GPU) for solution of the initial value problems of ordinary differential equations. Two cases are discussed: parallel solution of a single ODE and parallel execution of scalar ODE solvers. Whereas the advantages of the special architecture in the case of a single ODE are problematic, repeated solution of a single ODE for different data can profit from the parallel...
Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between...
Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response
In this paper, we consider a within-host model of malaria with Holling type II functional response. The model describes the dynamics of the blood-stage of parasites and their interaction with host cells, in particular red blood cells and immune effectors. First, we obtain equilibrium points of the system. The global stability of the disease-free equilibrium point is established when the basic reproduction ratio of infection is R₀< 1. Then the disease is controllable and dies out. In the absence...
Mathematical analysis of the optimizing acquisition and retention over time problem
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...
Mathematical analysis of the optimizing acquisition and retention over time problem
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...
Mathematical aspects of modeling self-oscillations of the heterogeneous catalytic reaction rate. I.