Results 41 to 50 of about 319 (72)

Estimates of some applicable inequalities on time scales [PDF]

arXiv, 2015
The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.
arxiv  

Halanay type inequalities on time scales with applications

, 2011
This paper aims to introduce Halanay type inequalities on time scales. By means of these inequalities we derive new global stability conditions for nonlinear dynamic equations on time scales. Giving several examples we show that beside generalization and
Adıvar, Murat, Bohner, Elvan Akın
core   +1 more source

Generalized ordinary differential equations in metric spaces [PDF]

arXiv, 2018
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back to Euclidean spaces.
arxiv  

Quasi-semigroups of operators on homogeneous time scales

Nonautonomous Dynamical Systems
This article discusses the concept of quasi-semigroups of bounded linear operators within the framework of time scales, encompassing both continuous and discrete cases.
Montenegro Sandra, Moya Ambrosio Tineo, Leiva Hugo   +2 more
doaj   +1 more source

Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales

, 2015
In this paper, we consider the almost periodic dynamics of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales. By establishing some dynamic inequalities on time scales, a permanence result for the model is obtained ...
Li, Yongkun, Wang, Pan
core   +1 more source

Some implications of a new definition of the exponential function on time scales

, 2010
We present a new approach to exponential functions on time scales and to timescale analogues of ordinary differential equations. We describe in detail the Cayley-exponential function and associated trigonometric and hyperbolic functions. We show that the
Cieśliński, Jan L.
core  

Hyers-Ulam stability of second-order linear dynamic equations on time scales [PDF]

Communications in Applied Analysis, Volume 16, 2012, pages 281-292, 2010
We establish the stability of second-order linear dynamic equations on time scales in the sense of Hyers and Ulam. To wit, if an approximate solution of the second-order linear equation exists, then there exists an exact solution to the dynamic equation that is close to the approximate one.
arxiv  

Multiple positive solutions for first-order impulsive integral boundary value problems on time scales

Boundary Value Problems, 2011
In this paper, we first present a class of first-order nonlinear impulsive integral boundary value problems on time scales. Then, using the well-known Guo-Krasnoselskii fixed point theorem and Legget-Williams fixed point theorem, some criteria for the ...
Li Yongkun, Shu Jiangye
doaj  

Delta-Nabla Isoperimetric Problems [PDF]

Int. J. Open Probl. Comput. Sci. Math. 3 (2010), no. 4, 124--137, 2010
We prove general necessary optimality conditions for delta-nabla isoperimetric problems of the calculus of variations.
arxiv  

On the non--multiplicity of solutions to matrix equations on time scales [PDF]

arXiv, 2012
In this paper we establish the non--multiplicity of solutions to first order matrix dynamic equations on time scales. The new results verify and extend the notions developed in \cite{thesis} to more complex systems of $n^2$ matrices with the help of ideas developed in \cite[Chap 5]{BP}, identifying Lipschitz conditions suitable to generalised $n^2 ...
arxiv