An application of Lyapunov–Razumikhin method to behaviors of Volterra integro-differential equations

Nieto, Juan J.; Tunç, Osman

doi:10.1007/s13398-021-01131-2

Cited by 7 publications

(2 citation statements)

References 46 publications

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“…(10) Thus, it is obvious that d dt ∆ 1 (t, x t ) is negative definite. From the inequality (10), it follows that assumption (A3) of ( [32, Theorem 4.2.9], Tunç et al [23,Theorem 1]) is satisfied. Thus, all the assumptions of ( [32, Theorem 4.2.9], Tunç et al [23,Theorem 1]) are held.…”

Section: Stability and Integrabilitymentioning

confidence: 99%

“…There are many publications on fundamental properties of solutions of FDEs, ODEs and so on. We cite here the papers [1][2][3][4][5][6], [7][8][9], [10], and the books of ( [32], [33][34][35][36][37][38][39]) fully or partially devoted to fundamental motions of trajectories of solutions of these classes of equations. In particular, UAS and boundedness of solutions at the infinity describe long time behaviors of solutions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability tests and solution estimates for non-linear differential equations

Tunç

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This article deals with certain systems of delay differential equations (DDEs) and a system of ordinary differential equations (ODEs). Here, five new theorems are proved on the fundamental properties of solutions of these systems. The results on the properties of solutions consist of sufficient conditions and they dealt with uniformly asymptotically stability (UAS), instability and integrability of solutions of unperturbed systems of DDEs, boundedness of solutions of a perturbed system of DDEs at infinity and exponentially stability (ES) of solutions of a system of nonlinear ODEs. Here, the techniques of proofs depend upon the Lyapunov- Krasovski? functional (LKF) method and Lyapunov function (LF) method. For illustrations, in particular cases, four examples are constructed as applications. Some results of this paper are given at first time in the literature, and the other results generalize and improve some related ones in the literature.

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Section: Stability and Integrabilitymentioning

confidence: 99%