Positive Solutions of a Class of Second Order Semilinear Elliptic Equations in the Plane.
Practical -stability behavior of time-varying nonlinear systems
We deal with the problem of practical uniform -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results.
Problème spectral inverse et équation de Szegö cubique
Dans un exposé précédent [1], nous avons justifié l’introduction de l’équation de Szegö cubique comme cas modèle d’équation de type Schrödinger sans dispersion. Ce cas modèle s’est révélé être intéressant sous divers aspects [2]. Dans cet exposé, nous nous attacherons à montrer comment la complète intégrabilité de l’équation de Szegö cubique permet de résoudre un problème spectral inverse pour les opérateurs de Hankel.
Proof of the De Gennes formula for the superheating field in the weak κ limit
Properties of the Nonoscillatory Solution for a Third Order Nonlinear Differential Equation
Propriétés asymptotiques d'un système d'équations différentielles
Quadratic homogeneous ODE systems of Jordan-rigid body type.
Qualitative behavior of a class of second order nonlinear differential equations on the halfline
A differential equation of the form (q(t)k(u)u')' = F(t,u)u' is considered and solutions u with u(0) = 0 are studied on the halfline [0,∞). Theorems about the existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
Qualitative behavior of a generalized Emden-Fowler differential system
Qualitative investigation of nonlinear differential equations describing infiltration of water
A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.
Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation.
Raman laser : mathematical and numerical analysis of a model
In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.
Raman laser: mathematical and numerical analysis of a model
In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.
Rational Constants of Generic LV Derivations and of Monomial Derivations
We describe the fields of rational constants of generic four-variable Lotka-Volterra derivations. Thus, we determine all rational first integrals of the corresponding systems of differential equations. Such systems play a role in population biology, laser physics and plasma physics. They are also an important part of derivation theory, since they are factorizable derivations. Moreover, we determine the fields of rational constants of a class of monomial derivations.
Recent results concerning dynamic equations on time scales.
Reducibility and characterization of symplectic Runge-Kutta methods.
Regularly varying solutions of generalized Thomas-Fermi equations
Regulatory network of drug-induced enzyme production: parameter estimation based on the periodic dosing response measurement
The common goal of systems pharmacology, i.e. systems biology applied to the field of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens et al. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system...
Remark in connection with an article of G. G. Hamedani: “Global existence of solutions of certain functional-differential equations” [Časopis Pěst. Mat. 106 (1981), 48-51]
Remark to transformations of linear differential and functional-differential equations
For linear differential and functional-differential equations of the -th order criteria of equivalence with respect to the pointwise transformation are derived.