Abstract
In this work, we develop the criteria for existence of Ψ- bounded solutions of system of linear dynamic equations on time scales. The advantage of results in this dynamical system is it unifies discrete as well as continuous systems. Initially, we develop if and only if conditions for the existence of at least one Ψ-bounded solution for linear dynamic equation y∆(τ ) = P (τ )y +g(τ ), for each Ψ- delta integrable Lebesgue function g, on time scale T +. Later, we obtain asymptotic nature of Ψ-bounded solutions of dynamical system. Also we provided the examples for supporting the results.AMS Subject Classification: 74H20, 34N05, 34C11
Highlights
The time scale(measure chains) calculus was initially developed and introduced by Stefan Hilger [9]
Coppel [5] developed the results of this model, for nonlinear and linear differential equations and Agarwal [1] developed for difference equations
Many authors [3, 4, 7, 10] developed the concept of Ψ-bounded solutions for the systems of linear difference equations an ordinary differential equations
Summary
The time scale(measure chains) calculus was initially developed and introduced by Stefan Hilger [9]. We present the results unify the existence of Ψ - bounded solutions of linear difference equations [8] and linear differential equations [6]. [2] Let the matrix valued function P on time scale T of order m × n. These values are Ψ-bounded solution of system (2) on T + at τ = v let Y2 be an arbitrary fixed subspace of Rd, supplementary to Y1.
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