Rosana Rodríguez-López

CONTRACTIVE MAPPING THEOREMS IN PARTIALLY ORDERED SETS AND APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS

We prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution. To this aim, we prove an appropriate fixed point theorem in partially ordered sets.

Fixed point theorems in ordered abstract spaces

We extend some fixed point theorems in L-spaces, obtaining extensions of the Banach fixed point theorem to partially ordered sets.

Existence of Periodic Solution for a Nonlinear Fractional Differential Equation

We study the existence of solutions for a class of fractional differential equations. Due to the singularity of the possible solutions, we introduce a new and proper concept of periodic boundary value conditions. We present Greens function and give some existence results for the linear case and then we study the nonlinear problem.

Boundary value problems for a class of impulsive functional equations

This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differential equations with maximum and integro-differential equations. In this paper, we also prove that the Lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval. The corresponding results are established for the impulsive case. The general formulation includes several types of functional dependence (delay equations, equations with maxima, integro-differential equations). Finally, we consider the case of functional dependence which is given by nonincreasing and bounded functions.

Variation of constant formula for first order fuzzy differential equations

In this paper, we study first order linear fuzzy differential equations by using the generalized differentiability concept and we present the general form of their solutions. We also correct and complete some previous results. Finally, some examples are given to illustrate our results.

Remarks on periodic boundary value problems for functional differential equations

We extend some results on existence and approximation of solution for a class of first-order functional differential equations with periodic boundary conditions. We show the validity of the monotone iterative technique under weaker hypotheses and present some examples.

Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions

Abstract This paper is concerned with the existence and approximation of solutions for a class of first-order functional differential equations with periodic boundary conditions. We present a new comparison result and extend previous results.

LINEAR FIRST-ORDER FUZZY DIFFERENTIAL EQUATIONS

We give the expression for the solution to some particular initial value problems in the space E1 of fuzzy subsets of ℝ. We deduce some interesting properties of the diameter and the midpoint of the solution and compare the solutions with the corresponding ones in the crisp case.

Monotone method for first-order functional differential equations

We study periodic boundary value problems relative to a general class of first-order functional differential equations. For this class of problems, we develop the monotone iterative technique. Our formulation is very general, including delay differential equations, functional differential equations with maxima and integro-differential equations, but the case where the operator defining the functional dependence is not necessarily Lipschitzian is also considered.

Existence of solutions to boundary value problem for impulsive fractional differential equations

In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fractional order differential equations. The notions of classical and weak solutions are introduced. Then, existence results of at least one and three solutions are proved.