Abstract
In this paper, we establish some new criteria on the boundedness and asymptotic constancy of solutions for a class of scalar neutral functional differential equations with time-varying delays via differential inequality techniques. Our results are an improvement of existing ones and generalization of the Haddock conjecture.
Highlights
Consider the following scalar neutral functional differential equation (NFDE)[x(t) − px(t − r)] = −F (x(t)) + F (x(t − r)), (1.1)where F : R → R is a continuous and strictly increasing function
Liu [4, 5] corrected these two propositions, and successfully used them to analyze the asymptotic behavior of some functional differential equations
Since the asymptotic behavior of NFDE with time-varying delays has not been touched in [1,3,6,8,9,10,11,12,13,14,15], one can find that the analysis method of the dynamical systems in the above references cannot be applied to prove x1 3 satisfies (1.5), it follows from Theorem
Summary
Academy of Intelligent Software, Guangzhou University, Guangdong Provincial Engineering Technology Research Center for Mathematical Educational Software Guangzhou 510006, China. Received March 8, 2017; revised June 9, 2017; published online September 15, 2017
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