Results 1 to 10 of about 200 (37)
From Hardy to Rellich inequalities on graphs
Proceedings of the London Mathematical Society, Volume 122, Issue 3, Page 458-477, March 2021., 2021 Abstract We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality.
Matthias Keller +2 more
wiley +1 more source
Variational approach to second-order impulsive dynamic equations on time scales [PDF]
, 2013 The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to nonlinear impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also we will be interested
Otero-Espinar, Victoria +1 more
core +3 more sources
Asymptotic properties for Volterra integro-dynamic systems [PDF]
, 2015 Using the resolvent matrix, a comparison principle and a useful equivalent system, we investigate the asymptotic behavior of linear Volterra integro-dynamic systems on time ...
Mirza, Safia +3 more
core +4 more sources
Backward Linear Control Systems on Time Scales
, 2010 We show how a linear control systems theory for the backward nabla differential operator on an arbitrary time scale can be obtained via Caputo's duality. More precisely, we consider linear control systems with outputs defined with respect to the backward
Pawluszewicz, Ewa, Torres, Delfim F. M.
core +1 more source
The contingent epiderivative and the calculus of variations on time scales
, 2010 The calculus of variations on time scales is considered. We propose a new approach to the subject that consists in applying a differentiation tool called the contingent epiderivative.
Girejko, Ewa +2 more
core +1 more source
A General Backwards Calculus of Variations via Duality
, 2010 We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale.
A.B. Malinowska +19 more
core +1 more source
Positive solutions for multi point impulsive boundary value problems on time scales [PDF]
, 2019 In this paper, we consider nonlinear second-order multi-point impulsive boundary value problems on time scales. We establish the criteria for the existence of at least one, two and three positive solutions by using the Leray-Schauder fixed point theorem,
Yaslan, İsmail
core +1 more source
A unified approach to the calculus of variations on time scales
, 2010 In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing the composition
Girejko, Ewa +2 more
core +1 more source
Wiman’s formula for a second order dynamic equation [PDF]
, 2014 We derive Wiman’s asymptotic formula for the number of generalized zeros of (nontrivial) solutions of a second order dynamic equation on a time scale. The proof is based on the asymptotic representation of solutions via exponential functions on a time ...
Alan Peterson +2 more
core +2 more sources
On uniqueness of the Laplace transform on time scales [PDF]
, 2011 After introducing the concept of null functions, we shall present a uniqueness result in the sense of the null functions for the Laplace transform on time scales with arbitrary graininess.
Karpuz, Basak
core +1 more source