On doubly nonlocal fractional elliptic equations

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

This work is devoted to the study of the existence of solutions to nonlocal equations involving the fractional Laplacian. These equations have a variational structure and we find a nontrivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. In addition, we require rather general assumptions on the local operator. As far as we know, this result is new and represent a fractional version of a classical theorem obtained working with Laplacian equations.

• Language: English
• Keywords: partial differential equations, quasilinear elliptic equations, nonlocal problems, fractional equations, Mountain Pass Theorem
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2015
• Number of pages: Str. 161-176
• Numbering: Vol. 26, iss. 2
• PID: 20.500.12556/RUL-111247
• UDC: 517.956
• ISSN on article: 1120-6330
• DOI: http://dx.doi.org/10.4171/RLM/700
• COBISS.SI-ID: 17294425
• Publication date in RUL: 26.09.2019

Record is a part of a journal

• Title: Atti della Accademia nazionale dei Lincei
• Shortened title: Atti Accad. naz. Lincei, Rend. Lincei, Mat. appl.
• Publisher: Accademia nazionale dei Lincei, EMS Publishing House
• ISSN: 1120-6330
• COBISS.SI-ID: 15928665