Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
Volume 7, Issue 4, Pages 593-616Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdss.2014.7.593
Keywords
Non Archimedean Mathematics; Non Standard Analysis; ultrafunctions; generalized solutions; critical points; differential operator; boundary value problem; material point
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Funding
- Austrian Science Fund FWF [P25311-N25]
- Austrian Science Fund (FWF) [P25311] Funding Source: Austrian Science Fund (FWF)
- Austrian Science Fund (FWF) [P 25311] Funding Source: researchfish
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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.
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