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An abstract Cauchy problem for higher order functional differential inclusions with infinite delay

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The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.
  • Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
  • Faculty of Mathematics, Voronezh State University, Universitetskays pl. 1, 394006 Voronezh, Russia
  • Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
  • Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan
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