Ψ-bounded solutions for a Lyapunov matrix differential equation

Diamandescu, Aurel

doi:10.14232/ejqtde.2009.1.17

Cited by 12 publications

(11 citation statements)

References 2 publications

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“…Definition 5. [7] Let u : T +  R d be a function is said to be Lebesgue Ψdeltaintegrable on T + provided u is delta measurable and u is Lebesgue deltaintegrable on…”

Section: Definition 3 [2]mentioning

confidence: 99%

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Existence of Î¨-bounded Solutions for System of Linear Dynamic equations on Time Scales

Rao¹,

Prasad²

2018

IJET

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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

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“…Definition 5. [7] Let u : T +  R d be a function is said to be Lebesgue Ψdeltaintegrable on T + provided u is delta measurable and u is Lebesgue deltaintegrable on…”

Section: Definition 3 [2]mentioning

confidence: 99%

“…Many authors [3,4,7,10] developed the concept of Ψ-bounded solutions for the systems of linear difference equations also an ordinary differential equations. Now we present the results unify the existence of Ψ -bounded solutions of linear difference equations [8] and linear differential equations [6].…”

Section: Introductionmentioning

confidence: 99%

Existence of Î¨-bounded Solutions for System of Linear Dynamic equations on Time Scales

Rao¹,

Prasad²

2018

IJET

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“…Thus, the trivial solution of the equation (1.1) is Ψ-strongly stable on R + . Ä ÑÑ 2.8º ( [5]) Let X(t) and Y (t) be a fundamental matrices for the equa-…”

Section: And Only If the Vector Valued Function Z(t) = Vec(z(t)) Is Amentioning

confidence: 99%

“…Recent results for Ψ-boundedness, Ψ-stability, dichotomy and conditioning for Lyapunov matrix differential equations have been given in [5], [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations

Diamandescu¹

2015

Mathematica Slovaca

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“…Recent works for Ψ− boundedness and Ψ− stability, dichotomy and conditioning for Lyapunov matrix differential equations have been given by M.S.N. Murty, G. Suresh Kumar and A. Diamandescu in [5], [13], [14]. In our paper [6] have been proved (necessary and) sufficient conditions for Ψ− (uniform) stability of the trivial solutions of (nonlinear) Lyapunov matrix differential equations (1), (2) and (3).…”

Section: Introductionmentioning

confidence: 99%