TY - JOUR
T1 - Generalized solutions of variational problems and applications
AU - Benci, Vieri
AU - Luperi Baglini, Lorenzo
AU - Squassina, Marco
PY - 2020
Y1 - 2020
N2 - Ultrafunctions are a particular class of generalized functions defined on a hyperreal field ℝ∗ ⊃ 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.
AB - Ultrafunctions are a particular class of generalized functions defined on a hyperreal field ℝ∗ ⊃ 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.
KW - nonstandard analysis
KW - nonstandard analysis
UR - http://hdl.handle.net/10807/154879
U2 - 10.1515/anona-2018-0146
DO - 10.1515/anona-2018-0146
M3 - Article
SN - 2191-9496
SP - 124
EP - 147
JO - Advances in Nonlinear Analysis
JF - Advances in Nonlinear Analysis
ER -