Global attractivity of nonlinear delay dynamic equations on time scales via Lyapunov functional method
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Nour H. M. Alsharif
Abstract
In this paper, we consider the nonlinear dynamic equation with variable delay
where 𝕋 is a time scale unbounded above, τ is an rd-continuous delay function and F is rd-continuous in its first component and continuous in its second component. We investigate the global attractivity of the trivial solution of (∗) by the well-known Lyapunov’s functional method. Our research significantly enhances and expands upon various established results in the literature, presents new results on time scales by defining a new companion function, and offers original perspectives for nonlinear delay dynamic equations on time scales. In addition, we present some illustrative examples on time scales to showcase the applicability of the new results.
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(Communicated by Irena Jadlovská)
References
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Articles in the same Issue
- Joins of normal matrices, their spectrum, and applications
- On isbell’s density theorem for bitopological pointfree spaces II
- Every positive integer is a sum of at most n + 2 centered n-gonal numbers
- A generalisation of q-additive functions
- Generalised class groups in dihedral and fake ℤp-extensions
- Singular value bounds with applications to norm and numerical radius inequalities
- Coefficient bounds for convex functions associated with cosine function
- On solutions to q-difference equations for q-appell functions in the spirit of Olsson and Exton
- Numerical implementation of solving a boundary value problem including both delay and parameter
- Solutions of second order iterative boundary value problems with nonhomogeneous boundary conditions
- Global attractivity of nonlinear delay dynamic equations on time scales via Lyapunov functional method
- On pseudo almost periodic solutions of the parabolic-elliptic Keller-Segel systems
- A note on derivations into annihilators of the ideals of banach algebras
- Characterization of nonlinear mixed skew lie and jordan n-Type derivation on ∗-Algebras
- Linear and uniformly continuous surjections between Cp-spaces over metrizable spaces
- A goodness-of-fit test for testing exponentiality based on normalized dynamic survival extropy
- Monotonicity results of ratio between two normalized remainders of Maclaurin series expansion for square of tangent function
