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.
Rearrangements of the coefficients of ordinary differential equations.
Reducible functional differential equations.
Relations among various criteria of uniqueness for ordinary differential equations
Relations between generalized solutions of ordinary differential equations
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]
Remarks concerning Driver's equation
We consider uniqueness for the initial value problem x' = 1 + f(x) - f(t), x(0) = 0. Several uniqueness criteria are given as well as an example of non-uniqueness.
Remarks concerning J. Witte's theorem and its applications
Remarks on generalized solutions of ordinary linear differential equations in the Colombeau algebra
In this paper first order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in , where denotes the Colombeau algebra.
Remarks on the uniqueness of second order
We are concerned with the uniqueness problem for solutions to the second order ODE of the form , subject to appropriate initial conditions, under the sole assumption that is non-decreasing with respect to , for each fixed. We show that there is non-uniqueness in general; on the other hand, several types of reasonable additional assumptions make the problem uniquely solvable. The interest in this problem comes, among other, from the study of oscillations of lumped parameter systems with implicit...
Remarque sur la méthode de la variation de la constante généralisée
Remarques sur les solutions générales des équations différentielles
Representation of the set of mild solutions to the relaxed semilinear differential inclusion
We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.