Some hemivariational inequalities in the Euclidean space

Molica Bisci, Giovanni (author), Repovš, Dušan (author)

The purpose of this paper is to study the existence of weak solutions for some classes of hemivariational problems in the Euclidean space ▫$\mathbb{R}^d \, (d \ge 3)$▫. These hemivariational inequalities have a variational structure and, thanks to this, we are able to find a non-trivial weak solution for them by using variational methods and a non-smooth version of the Palais principle of symmetric criticality for locally Lipschitz continuous functionals, due to Krawcewicz and Marzantowicz. The main tools in our approach are based on appropriate theoretical arguments on suitable subgroups of the orthogonal group ▫$O(d)$▫ and their actions on the Sobolev space ▫$H^1(\mathbb{R}^d)$▫. Moreover, under an additional hypotheses on the dimension d and in the presence of symmetry on the nonlinear datum, the existence of multiple pairs of sign-changing solutions with different symmetries structure has been proved. In connection to classical Schrödinger equations a concrete and meaningful example of an application is presented.

• Language: English
• Keywords: hemivariational inequalities, variational methods, principle of symmetric criticality, radial solutions, non-radial solutions
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: Str. 958-977
• Numbering: Vol. 9, iss. 1
• PID: 20.500.12556/RUL-109017
• UDC: 517.956
• ISSN on article: 2191-9496
• DOI: 10.1515/anona-2020-0035
• COBISS.SI-ID: 18703961
• Publication date in RUL: 19.08.2019

Record is a part of a journal

• Title: Advances in nonlinear analysis
• Publisher: De Gruyter
• ISSN: 2191-9496
• COBISS.SI-ID: 16253785