Globally exponential stability of piecewise pseudo almost periodic solutions for neutral differential equations with impulses and delays. (English) Zbl 1496.34108
Impulsive differential equations are very important class of differential equations whose dynamics is very rich. In this work, authors consider a delayed impulsive neutral differential equations. The coefficients are assumed to be bounded. The main objective is to establish the existence of piecewise pseudo almost periodic solution. The techniques used are contraction mapping principle and generalized Gronwall-Bellmain inequality. Moreover, the stability of such solution is also shown. The stability is globally exponential. At the end, an example with numerical illustration is provided by the authors.
Reviewer: Syed Abbas (Mandi)
MSC:
| 34K14 | Almost and pseudo-almost periodic solutions to functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 34K45 | Functional-differential equations with impulses |
| 34K20 | Stability theory of functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
piecewise pseudo almost periodic solution; neutral differential equations; impulse; globally exponential stabilityReferences:
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