Suppose that T is a bounded operator on a nonzero Banach space X . Given a vector x ∈ X , we say that x is hypercyclic for T if the orbit OrbTx = {T x}n is dense in X . Similarly, x is said to be weakly hypercyclic if OrbTx is weakly dense in X . A bounded operator is called hypercyclic or weakly hypercyclic if it has a hypercyclic or, respectively, a weakly hypercyclic vector. It is shown in [...

This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay differential equations (DDEs). We show that the linearized collocation system is equivalent to a discretization of the linearized periodic boundary value problem (BVP). This linear BVP is solved using the Newton-Picard single shooting method ([Int. J. Bif...

In this paper, we prove a result of existence and uniqueness solutions for the following class problem initial value differential equations with maxima Caputo?s fractional order on time scales: c??a u(?) = ?(?, u(?), max ??[a,?] u(?)), ? J := [a, b]T, 0 < 1, u(a) ?, We used techniques Picard weakly operators to obtain some data dependency parameters results.

In this paper, we show that injectivity with respect to the class $mathcal{D}$  of dense monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary category  well-behaves. Indeed, if $mathcal{M}$ is a subclass of monomorphisms, $mathcal{M}cap mathcal{D}$-injectivity  well-behaves. We also introduce the notion of $(r,t)$-injectivity in the category {bf S-Act}, where $r...

We prove that any bounded linear operator on Lp[0, 1] for 1 6 p < ∞, commuting with the Volterra operator V , is not weakly supercyclic, which answers affirmatively a question raised by Léon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with V . ...

Let E be an ideal of L0 over a σ-finite measure space (Ω,Σ, μ), and let E∼ stand for the order dual of E. For a real Banach space (X, ‖ · ‖X ) let E(X) be a subspace of the space L0(X) of μ-equivalence classes of strongly Σ-measurable functions f : Ω −→ X and consisting of all those f ∈ L0(X) for which the scalar function ‖f(·)‖X belongs to E. For a real Banach space (Y, ‖ · ‖Y ) a linear opera...