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.
Self similar solutions of generalized Burgers equation.
Semilinear evolution equations of the parabolic type
This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
Set differential equations with causal operators.
Set-valued fractional order differential equations in the space of summable functions
In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type , a.e. on (0,1), , αₙ ∈ (0,1), where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.
Singularity diferenciální rovnice
Singularity diferenciální rovnice. II
Sobre la aplicación del teoerma de Picard a una ecuación diferencial de orden n.
Solute transport in porous media with equilibrium and non-equilibrium multiple-site adsorpition: Travelling weaves.
Solution dependence on problem parameters for initial-value problems associated with the Stieltjes Sturm-Liouville equations.
Solutions of initial value problems for a pair of linear first order ordinary differential systems with interface-spatial conditions.