# American Institute of Mathematical Sciences

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September  2010, 14(2): 629-654. doi: 10.3934/dcdsb.2010.14.629

## Mutational inclusions: Differential inclusions in metric spaces

 1 Institute of Mathematics, Johann Wolfgang Goethe University, 60054 Frankfurt (Main), Germany

Received  June 2009 Revised  September 2009 Published  June 2010

The focus of interest is how to extend ordinary differential inclusions beyond the traditional border of vector spaces. We aim at an existence theorem for solutions whose values are in a given metric space.
In the nineties, Aubin suggested how to formulate ordinary differential equations and their main existence theorems in metric spaces: mutational equations (which are quite similar to the quasidifferential equations of Panasyuk). Now the well-known Antosiewicz-Cellina Theorem is extended to so-called mutational inclusions. It provides new results about nonlocal set evolutions in R N .
Citation: Thomas Lorenz. Mutational inclusions: Differential inclusions in metric spaces. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 629-654. doi: 10.3934/dcdsb.2010.14.629
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