Generalized solutions of variational problems and applications-Reference-Cited by-同舟云学术

Generalized solutions of variational problems and applications

Published:2018-08-08 Issue:1 Volume:9 Page:124-147
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Benci Vieri¹,Luperi Baglini Lorenzo²^ORCID,Squassina Marco³

Affiliation:

1. Dipartimento di Matematica , Università degli Studi di Pisa , Via F. Buonarroti 1/c, 56127 Pisa ; and Centro Linceo interdisciplinare Beniamino Segre, Palazzo Corsini – Via della Lungara 10, 00165 Roma , Italy

2. Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1, 1090 Wien , Austria

3. Dipartimento di Matematica e Fisica , Università Cattolica del Sacro Cuore , Via dei Musei 41, 25121 Brescia , Italy

Abstract

Abstract 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.

Funder

Austrian Science Fund

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Reference23 articles.

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4. V. Benci and L. Luperi Baglini, A model problem for ultrafunctions, Proceedings of the Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems, Electron. J. Differ. Equ. Conf. 21 Texas State University, San Marcos (2014), 11–21.

5. V. Benci and L. Luperi Baglini, Basic properties of ultrafunctions, Analysis and Topology in Nonlinear Differential Equations, Progr. Nonlinear Differential Equations Appl. 85, Birkhäuser/Springer, Cham (2014), 61–86.

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