Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type. (English) Zbl 1428.34087
Summary: In this paper, we prove the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of a class of higher order nonlinear delay differential equations with multiple bounded variable delays on a compact interval. Result of existence and uniqueness of solution is obtained by fixed point approach. Meanwhile, for the first time, integral inequality of Grönwall-Bellman-Bihari’s type with delay is applied to prove the stability theorem which made our results more generalized and interesting.
MSC:
| 34K05 | General theory of functional-differential equations |
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 34D10 | Perturbations of ordinary differential equations |
Keywords:
Hyers-Ulam stability; Hyers-Ulam-Rassias stability; nonlinear delay differential equations; Picard operator; Grönwall-Bellman-Bihari’s integral inequalityReferences:
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