Fixed points and stability in neutral differential equations with variable delays |
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| Authors: | Chuhua Jin Jiaowan Luo |
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| Institution: | Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong 510090, People's Republic of China ; Corresponding author. School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, People's Republic of China |
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| Abstract: | In this paper we consider a linear scalar neutral delay differential equation with variable delays and give some new conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. The results of Burton, Raffoul, and Zhang are improved and generalized. |
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| Keywords: | Fixed points stability neutral delay differential equations variable delays |
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