Now showing items 1-11 of 11

  • Converses of copson's inequalities on time scales 

    Saker, Samir H.; 'Regan, Donal; Agarwal, Ravi P. (Element d.o.o., 2015-01-01)
    In this paper, we will prove some new dynamic inequalities on a time scale T. These inequalities when T = N contain the discrete inequalities due to Bennett and Leindler which are converses of Copson's inequalities. The ...
  • Evolution equations with causal operators 

    Agarwal, Ravi P.; Arshad, Sadia; Lupulescu, Vasile; 'Regan, Donal (Element d.o.o., 2015-01-01)
    In this paper we present an existence result for causal functional evolution equations. The result is obtained under a condition with respect to the Hausdorff measure of noncompactness. An application with partial differential ...
  • Existence of solutions for an elliptic boundary value problem via a global minimization theorem on hilbert spaces 

    Ayadi, Souad; Moussaoui, Toufik; 'Regan, Donal (Element d.o.o., 2016-01-01)
    We present a new global minimization theorem on Hilbert spaces which is different from the one in Hofer [7] using the notion of a nonexpansive potential operator. An example is given to illustrate our result.
  • Higher order dynamic inequalities on time scales 

    Saker, Samir H.; Agarwal, Ravi P.; 'Regan, Donal (Element d.o.o., 2014-01-01)
    In this paper, we will prove some new dynamic inequalities of higher orders on time scales. The results contain some continuous and discrete inequalities as special cases. We will prove the results by making use of Holder's ...
  • Minimization principle in ordered banach spaces and application via ekeland's variational principle 

    Boucenna, Amina; Briki, Mabrouk; Moussaoui, Toufik; 'Regan, Donal (Element d.o.o., 2017-01-01)
    In this paper we establish a minimization principle in an ordered Banach space (in particular in a Riesz-Banach space). As an application we discuss the existence of a positive solution for a boundary value problem on the ...
  • New hilbert dynamic inequalities on time scales 

    Saker, Samir H.; Ahmed, A. M.; Rezk, H. M.; 'Regan, Donal; Agarwal, Ravi P. (Element d.o.o., 2017-01-01)
    In this paper, we prove some new dynamic inequalities of Hilbert type on time scales. From these inequalities, as special cases, we will formulate some special integral and discrete inequalities. The main results are proved ...
  • New multiplicative higher order dynamic inequalities of opial type 

    Rabie, Safi S.; Saker, Samir H.; 'Regan, Donal; Agarwal, Ravi P. (Element d.o.o., 2016-01-01)
    In this paper, we prove some new multiplicative dynamic inequalities of Opial type on a time scale T. The main results will be proved by using Holder's inequality, the chain rule and some basic dynamic inequalities designed ...
  • Practical stability of caputo fractional differential equations by lyapunov functions 

    Agarwal, Ravi P.; Hristova, Snezhana G.; 'Regan, Donal (Element d.o.o., 2016-01-01)
    The practical stability of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov ...
  • Practical stability of differential equations with non-instantaneous impulses 

    Agarwal, Ravi P.; Hristova, Snezhana G.; 'Regan, Donal (Element d.o.o., 2017-01-01)
    The concept of practical stability is generalized to nonlinear differential equations with non-instantaneous impulses. These type of impulses start their action abruptly at some points and then continue on given finite ...
  • Some dynamic inequalities of hardy type on time scales 

    Saker, Samir H.; 'Regan, Donal; Agarwal, Ravi P. (Element d.o.o., 2014-01-01)
    In this paper we prove some new dynamic inequalities of Hardy type on time scales. The main results will be proved using algebraic inequalities, Holder inequality and Keller's chain rule on time scales.
  • Some new opial dynamic inequalities with weighted functions on time scales 

    Saker, Samir H.; Osman, M. M.; 'Regan, Donal; Agarwal, Ravi P. (Element d.o.o., 2015-01-01)
    In this paper we prove some new dynamic inequalities with two weight functions and some new dynamic inequalities with two unknown functions of Opial type on time scales. The main results will be proved by employing Holder's ...