# American Institute of Mathematical Sciences

August  2014, 7(4): 593-616. doi: 10.3934/dcdss.2014.7.593

## Ultrafunctions and applications

 1 Dipartimento di Matematica Applicata, Università degli Studi di Pisa, Via F. Buonarroti 1/c, Pisa, Italy 2 University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

Received  October 2013 Revised  December 2013 Published  February 2014

This paper deals with a new kind of generalized functions, called ultrafunctions", which have been introduced recently in [5] and developed in [10] and [11]. Their peculiarity is that they are based on a Non Archimedean field, namely on a field which contains infinite and infinitesimal numbers. Ultrafunctions have been introduced to provide generalized solutions to equations which do not have any solutions, not even among the distributions. Some applications of this kind will be presented in the second part of this paper.
Citation: Vieri Benci, Lorenzo Luperi Baglini. Ultrafunctions and applications. Discrete & Continuous Dynamical Systems - S, 2014, 7 (4) : 593-616. doi: 10.3934/dcdss.2014.7.593
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