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October  2014, 34(10): 4291-4321. doi: 10.3934/dcds.2014.34.4291

Skew-product semiflows for non-autonomous partial functional differential equations with delay

 1 Departamento de Matemática Aplicada, E. Ingenierías Industriales, Universidad de Valladolid, Paseo del Cauce 59, 47011 Valladolid 2 Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales and member of IMUVA, Instituto de Matemáticas, Universidad de Valladolid, 47011 Valladolid 3 Departamento de Didáctica de las Ciencias Experimentales, Sociales y de la Matemática, E.U. Educación, Universidad de Valladolid, 34004 Palencia, Spain

Received  January 2013 Revised  March 2013 Published  April 2014

A detailed dynamical study of the skew-product semiflows induced by families of AFDEs with infinite delay on a Banach space is carried over. Applications are given for families of non-autonomous quasimonotone reaction-diffusion PFDEs with delay in the nonlinear reaction terms, both with finite and infinite delay. In this monotone setting, relations among the classical concepts of sub and super solutions and the dynamical concept of semi-equilibria are established, and some results on the existence of minimal semiflows with a particular dynamical structure are derived.
Citation: Sylvia Novo, Carmen Núñez, Rafael Obaya, Ana M. Sanz. Skew-product semiflows for non-autonomous partial functional differential equations with delay. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4291-4321. doi: 10.3934/dcds.2014.34.4291
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