Analytic solutions of nonlinear neutral and advanced differential equations.
Another approach to the theory of differential inequalities realtive to changes in the initial times.
Antitone operators and ordinary differential equations
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 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...
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 limit cycle of differential systems with variable coefficients
The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.
Asymptotic behaviour of Riccati's differential equation associated with self-adjoint scalar equations of even order
Asymptotic equivalence and homeomorphism of the families of endomorphisms and surjections of the metrizable vector fibering
Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations.