On stability, boundedness, and square integrability of solutions of certain third order neutral differential equations

Graef, John R.; Beldjerd, Djamila; Remili, Moussadek

doi:10.21136/mb.2021.0081-19

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is widely used in many aspects, such as physical chemistry, mathematical biology, electrical control, and engineering; see [4][5][6][7][8]. Graef et al [9] studied the stability, boundedness, and square integrability of solutions of third-order neutraldelay differential equations. In 2022, Taie and Alwaleedy [10] dealt with the existence problems of a periodic solution for the third-order neutral functional differential equation:…”

Section: Introductionmentioning

confidence: 99%

Periodic Solution for a Kind of Third-Order Neutral-Type Differential Equation

Shu

2023

Journal of Function Spaces

View full text Add to dashboard Cite

In this paper, we investigate a class of a third-order neutral-type differential equation with time-varying delays. Some sufficient conditions on the existence of a periodic solution are established for the considered system. Different from the previously reported research results, by utilizing the properties of neutral operators and a special variable substitution, we transform a high-order neutral equation into a first-order three-dimensional nonneutral system. The existence of a periodic solution such as the high-order neutral equation has not been given much attention in past papers due to the difficulty of estimation of prior bounds of solutions. This paper is devoted to the use of properties of neutral-type operators with a variable parameter and Mawhin’s continuation theorem for overcoming the above difficulties. The neutral term in the third-order neutral differential equation in this paper contains a variable parameter which is different from third-order neutral-type equations that have been studied. The third-order neutral-type equation studied in this paper is more general, and similar equations studied in the past are special cases of the equations studied in this paper. Finally, an example is given to elucidate the effectiveness and values of the present results. Our results are new and complement the related results of third-order functional differential equations.

show abstract

Section: Introductionmentioning

confidence: 99%

Periodic Solution for a Kind of Third-Order Neutral-Type Differential Equation

Shu

2023

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

On stability, boundedness, and square integrability of solutions of certain third order neutral differential equations

Cited by 1 publication

References 0 publications

Periodic Solution for a Kind of Third-Order Neutral-Type Differential Equation

Periodic Solution for a Kind of Third-Order Neutral-Type Differential Equation

Contact Info

Product

Resources

About