Advanced Nonlinear Studies
Editor-in-Chief: Ahmad, Shair
IMPACT FACTOR 2017: 1.029
5-year IMPACT FACTOR: 1.147
CiteScore 2017: 1.29
SCImago Journal Rank (SJR) 2017: 1.588
Source Normalized Impact per Paper (SNIP) 2017: 0.971
Ultrafunctions and Generalized Solutions
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think of
with Dirichlet boundary conditions in a bounded open star-shaped set. Having this problem in mind, we construct a new class of functions called ultrafunctions in which the above problem has a (generalized) solution. In this construction, we apply the general ideas of Non Archimedean Mathematics (NAM) and some techniques of Non Standard Analysis. Also, some possible applications of ultrafunctions are discussed.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.