Measure functional differential equations with infinite delay |
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| Affiliation: | 1. Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India;2. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India;1. Université Gaston Berger de Saint-Louis, UFR SAT, Département de Mathématiques, Saint-Louis B. P. 234, Sénégal;2. École Polytechnique de Thiés, Département Tronc commun, Thiés BP A10, Sénégal;3. African Institute for Mathematical Sciences Ghana, P.O. Box LGDTD 20046, Summerhill Estates, East Legon Hills, Santoe, Acrra, Ghanna;4. Department of Mathematics, Gauhati University, Guwahati, Assam 781014, India |
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| Abstract: | We introduce measure functional differential equations with infinite delay and an axiomatically described phase space. We show how to transform these equations into generalized ordinary differential equations whose solutions take values in a suitable infinite-dimensional Banach space. Even in the special case of functional equations with finite delay, our result improves the existing one by imposing weaker conditions on the right-hand side. |
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