Victoria Otero-Espinar

Existence of Solutions for Fractional Differential Inclusions with Antiperiodic Boundary Conditions

We study the existence of solutions for a class of fractional differential inclusions with anti-periodic boundary conditions. The main result of the paper is based on Bohnenblust- Karlins fixed point theorem. Some applications of the main result are also discussed.

BASIC PROPERTIES OF SOBOLEV'S SPACES ON TIME SCALES

We study the theory of Sobolevs spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolevs spaces of functions defined on an arbitrary open interval of the real numbers are derived.

Existence and approximation of solutions for first-order discontinuous difference equations with nonlinear global conditions in the presence of lower and upper solutions☆

Abstract This paper is devoted to the study of the existence of solutions of first-order difference equations verifying nonlinear conditions that involve the global behavior of the solution. We prove that the existence of lower and upper solutions warrants the existence of such solutions lying in the sector formed by the mentioned functions. We also can prove that some classical results for differential equations are not true in general for this case.

Existence and approximation of solution of three-point boundary value problems on time scales

The method of upper and lower solutions and the generalised quasilinearization technique for second order nonlinear three-point time scale boundary value problems of the type are developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained.

Criteria for Existence and Nonexistence of Positive Solutions to a Discrete Periodic Boundary Value Problem

We are concerned with proving the existence of positive solutions of a periodic boundary value problem for a discrete nonlinear equation We shall also obtain criteria which leads to nonexistence of positive solutions. Index theory for the positive smooth function f and lower and upper solutions when the function f is allowed to have nonconstant sign and to be singular at 0 are employed.

Fixed sign solutions of second-order difference equations with Neumann boundary conditions

In this paper, we study the existence of solution of the nonlinear second-order difference problem with Neumann boundary conditions. Assuming the existence of a pair of ordered lower and upper solutions γ and β, we obtain optimal existence results for the case γ ≤ β and even for γ ≥ β. To this end, we do an exhaustive study of the values of the real parameters α and μ, for which the associated Greens function to the linear operator L[α,μ] uκ ≡ uκ+2 − 2 α uκ+1 + μ uκ with Neumann boundary conditions has fixed sign.

Multiple Positive Solutions in the Sense of Distributions of Singular BVPs on Time Scales and an Application to Emden-Fowler Equations

This paper is devoted to using perturbation and variational techniques to derive some sufficient conditions for the existence of multiple positive solutions in the sense of distributions to a singular second-order dynamic equation with homogeneous Dirichlet boundary conditions, which includes those problems related to the negative exponent Emden-Fowler equation.

Existence of extremal solutions by approximation to a first-order initial dynamic equation with Carathéodory's conditions and discontinuous non-linearities*

This paper is devoted to the study of the existence of extremal solutions to a first-order initial value problem on an interval of an arbitrary time scale. We prove the existence of extremal solutions for problems satisfying Carathéodorys conditions. Moreover, they are approximated uniformly by a sequence of lower and upper solutions to this problem, respectively. We also can warrant the existence and approximation of extremal solutions for the problem by relaxing their continuity properties.

Variational approach to second-order impulsive dynamic equations on time scales

The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to a nonlinear impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also, we are interested in the solutions of the impulsive nonlinear problem with linear derivative dependence satisfying an impulsive condition.MSC:34B37, 34N05.

Existence and Uniqueness of Positive Solution for Singular BVPs on Time Scales

This paper is devoted to derive some sufficient conditions for the existence and uniqueness of positive solutions to a singular second-order dynamic equation with Dirichlet boundary conditions.