# Second-order differentiability with respect to parameters for differential equations with adaptive delays

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DOI: 10.1007/s11464-010-0005-9

- Cite this article as:
- Chen, Y., Hu, Q. & Wu, J. Front. Math. China (2010) 5: 221. doi:10.1007/s11464-010-0005-9

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## Abstract

In this paper, we study the second-order differentiability of solutions with respect to parameters in a class of delay differential equations, where the evolution of the delay is governed explicitly by a differential equation involving the state variable and the parameters. We introduce the notion of locally complete triple-normed linear space and obtain an extension of the well-known uniform contraction principle in such spaces. We then apply this extended principle and obtain the second-order differentiability of solutions with respect to parameters in the *W*^{1,p}-norm (1 ⩽ *p* < ∞).