Application du principe du dernier multiplicateur à l'intégration d'une équation différentielle du second ordre
Application of Lakshmikantham's monotone-iterative technique to the solution of the initial value problem for impulsive integro-differential equations.
Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations
The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.
Application of matrix polynomials to investigation of singular equations.
Application of symbolic computation in nonlinear differential-difference equations.
Application of the Laplace transform to simulating continuous systems
Application of the Mean Ergodic Theorem to Certain Semigroups
Applications of contractive-like mapping principles to fuzzy equations
We recall a recent extension of the classical Banach fixed point theorem to partially ordered sets and justify its applicability to the study of the existence and uniqueness of solution for fuzzy and fuzzy differential equations. To this purpose, we analyze the validity of some properties relative to sequences of fuzzy sets and fuzzy functions.
Applications of Lie systems in quantum mechanics and control theory
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...
Applications of the Carathéodory theorem to PDEs
We discuss and exploit the Carathéodory theorem on existence and uniqueness of an absolutely continuous solution x: ℐ (⊂ ℝ) → X of a general ODE for the right-hand side ℱ : dom ℱ ( ⊂ ℝ × X) → X taking values in an arbitrary Banach space X, and a related result concerning an extension of x. We propose a definition of solvability of (*) admitting all connected ℐ and unifying the cases “dom ℱ is open” and “dom ℱ = ℐ × Ω for some Ω ⊂ X”. We show how to use the theorems mentioned above to get approximate...
Approssimabilità degli zeri di una funzione mediante gli zeri di una sua espressione asintotica. Applicazione alle soluzioni delle equazioni differenziali lineari del secondo ordine
Approximate and relaxed solutions of differential inclusions
Approximate solution of an inhomogeneous abstract differential equation
Recently, we have developed the necessary and sufficient conditions under which a rational function approximates the semigroup of operators generated by an infinitesimal operator . The present paper extends these results to an inhomogeneous equation .
Approximate solutions for integrodifferential equations of the neutral type
The main objective of the present paper is to study the approximate solutions for integrodifferential equations of the neutral type with given initial condition. A variant of a certain fundamental integral inequality with explicit estimate is used to establish the results. The discrete analogues of the main results are also given.
Approximate solutions of matrix differential equations.
A method for solving second order matrix differential equations avoiding the increase of the dimension of the problem is presented. Explicit approximate solutions and an error bound of them in terms of data are given.
Approximate solutions of the forced Duffing equation with mixed nonlinearities.
Approximation de quelques problèmes de type Stokes par une méthode d'èlements finis mixtes.
Approximation methods for solving the Cauchy problem
In this paper we give some new results concerning solvability of the 1-dimensional differential equation with initial conditions. We study the basic theorem due to Picard. First we prove that the existence and uniqueness result remains true if is a Lipschitz function with respect to the first argument. In the second part we give a contractive method for the proof of Picard theorem. These considerations allow us to develop two new methods for finding an approximation sequence for the solution....
Approximation of analytic functions by Kummer functions.
Approximation of attainable sets of an evolution inclusion of subdifferential type.