Differential equations on time scales
Positive Solutions to Singular and Delay Higher-Order Differential Equations on Time Scales
... We are concerned with singular three-point boundary value problems for delay higher-order dynamic equations on time scales. Theorems on the existence of positive solutions are obtained by utilizing ...
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Asymptotic behavior of solution for a fractional Riemann-Liouville differential equations on time scales
... A time scale T is an arbitrary nonempty closed subset of the real numbers. For t ∈ T, we define the forward jump operator σ : T → T by σ ( t ) = inf { s ∈ T : s > t } , and the backward jump operator ρ ( t ) = ...
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Antiperiodic Boundary Value Problem for Second Order Impulsive Differential Equations on Time Scales
... We should mention that 1.1, 1.2 are more general than equations considered in 13, 18 since f, J both contain x and its derivative. So our result is still new even when 1.1, 1.2 reduce to equations studied ...
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Basic theory of differential equations with linear perturbations of second type on time scales
... The details of different types of contractions appear in the monographs of Dhage [16] and Granas and Dugundji [17]. There do exist D-functions, and the commonly used D- functions are ϕ(t) = lt and ϕ(t) = 1+t t . These ...
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Basic theory of differential equations with mixed perturbations of the second type on time scales
... As far as we know, there are no results for the DETS (1). From the works mentioned we consider the theory of DETS (1). We give an existence theorem for the DETS (1) under Lipschitz conditions. We also present some ...
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Positive periodic solutions of Lotka Volterra like impulsive functional differential equations with infinite distributed time delays on time scales
... To the best of our knowledge, few papers have been published on the existence of posi- tive periodic solutions of system (.). Our main purpose of this paper is by using a fixed point theorem of strict-set contraction to ...
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Three Positive Periodic Solutions for a Class of Higher Dimensional Functional Differential Equations with Impulses on Time Scales
... differential equations with impulses on time scales of the following form: x Δ t Atxt ft, x t , t / t j , t ∈ T, xt j xt − j I j xt j , where At a ij t n×n is ...
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On the Perron Effect for Exponential Stability of Differential Systems on Time Scales
... dynamic equations on time scales was introduced by Stefan Hilger [2] in order to unify and extend results of differential equations, difference equations, q-difference ...
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Stability in Totally Nonlinear Neutral Dynamic Equations on Time Scales
... There is no doubt that the Lyapunov method have been used successfully to investigate stability properties of wide variety of ordinary, functional and partial equations. Nevertheless, the application of this ...
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Oscillation of higher order nonlinear dynamic equations on time scales
... are established in delay ξ( t ) ≤ t and non-delay ξ( t ) = t cases, where n ≥ 2 is a positive integer, l is the ratio of positive odd integers. Many of the results are new for the corresponding higher order difference ...
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Exponential Dichotomies and Fredholm Operators of Dynamic Equations on Time Scales
... dynamic equations on time scales was introduced by Stefan Hilger [21] in order to unify and extend results of differential equations, difference eq- uations, q -difference ...
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Some New Gronwall-Bellman Type And Volterra-Fredholm Type Fractional Integral Inequalities And Their Applications in Fractional Differential Equations
... type differential and integral inequalities [13-18], retarded inequalities [19-23], difference inequalities [24-28], Volterra- Fredholm type inequalities [24,27], and dynamic inequal- ities on time ...
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NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SYSTEMS OF COUPLED FRACTIONAL BVPS WITH p-LAPLACIAN
... ordinary differential equations, difference equations, dynamic equations on time scales, p-Laplacian, fractional order differential equations and boundary value ...
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Robust Stability of Implicit Dynamic Equations on Time Scales
... a time-varying differential-algebraic equation and if T then it is a time-varying implicit difference ...The differential-algebraic equations (DAEs) are the mathematical models ...
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Metric based upscaling for partial differential equations with a continuum of scales
... transport equations for reservoir modeling in geophysics is currently implemented in the industry and has been shown to be more accurate than local methods ([131] and ...is time independent and one has to ...
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Almost Sure Exponential Stability of Stochastic Differential Delay Equations on Time Scales
... stochastic differential/difference delay equations have come to play an important role in describing the evolution of eco-systems in random environment, in which the future state depends not only on the ...
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The method of finding solutions of partial dynamic equations on time scales
... dynamic equations on time ...the time scales q Z ...other time scales when the multiplication rule of two generalized poly- nomials on these time scales is ...
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Affine periodic solutions for nonlinear dynamic equations on time scales
... As a structural property of functions, the affine-periodicity is a generalization of pure periodicity. Recently, some existence theorems as regards affine-periodic solutions have been proved for APSs. We refer to [–]. ...
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Lyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales
... with the assumption of differentiability for ft, x. The main results of this paper are established in Section 3 where we deal with the stability of 1.5. The technique we use in this section is somewhat similar to the one ...
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A class of linear dynamical equations for a Banach space on time scales
... This delta derivative is equal to f (the usual derivative) if T = R, and it is equal to f (the usual forward difference) if T = Z . So, the study of dynamical equations on time scales allows a ...
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