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Stability results for nonlinear functional differential equations using fixed point methods |
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| Authors: | Guiling Chen Dingshi Li Onno van Gaans Sjoerd Verduyn Lunel |
| Affiliation: | 1. Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, PR China;2. Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA, Leiden, The Netherlands;3. Mathematical Institute, Utrecht University, P.O. Box 80010, 3508 TA, Utrecht, The Netherlands |
| Abstract: | We present new conditions for stability of the zero solution for three distinct classes of scalar nonlinear delay differential equations. Our approach is based on fixed point methods and has the advantage that our conditions neither require boundedness of delays nor fixed sign conditions on the coefficient functions. Our work extends and improves a number of recent stability results for nonlinear functional differential equations in a unified framework. A number of examples are given to illustrate our main results. |
| Keywords: | Fixed point theory Asymptotic stability Contraction mapping principle (neutral) integro-differential equation Variable delay |
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