Generalized solutions of variational problems and applications

Advances in Nonlinear Analysis

Luperi Baglini Lorenzo¹  Benci Vieri²  Squassina Marco³ 

[1] and Centro Linceo interdisciplinare Beniamino Segre,Palazzo Corsini – Via della Lungara 10, 00165 Roma, Italy;Dipartimento di Matematica, Università degli Studi di Pisa, Via F. Buonarroti 1/c, 56127Pisa;Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090Wien, Austria;

关键词: ultrafunctions;    non-archimedean mathematics;    nonstandard analysis;    delta function;    03h05;    26e35;    28e05;    46s20;   

DOI  :  10.1515/anona-2018-0146

来源: DOAJ

【 摘 要 】

Ultrafunctions are a particular class of generalized functions defined on a hyperreal field ℝ*⊃ℝ{\mathbb{R}^{*}\supset\mathbb{R}} that allow to solve variational problems with no classical solutions. We recall the construction of ultrafunctions and we study the relationships between these generalized solutions and classical minimizing sequences. Finally, we study some examples to highlight the potential of this approach.

【 授权许可】

Unknown