Nonlocal Kirchhoff superlinear equations with indefinite nonlinearity and lack of compactness

Li, Lin (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

We study the following Kirchhoff equation ▫$$ - \left( 1 + b \int_{\mathbb{R}^3} |\nabla u|^2 dx \right) \Delta u + V(x) u = f(x,u), \quad x \in \mathbb{R}^3. $$▫ A feature of this paper is that the nonlinearity ▫$f$▫ and the potential ▫$V$▫ are indefinite, hence sign-changing. Under some appropriate assumptions on ▫$V$▫ and ▫$f$▫, we prove the existence of two different solutions of the equation via the Ekeland variational principle and the mountain pass theorem.

• Language: English
• Keywords: mountain pass, Ekeland variational principle, nonlocal Kirchhoff equation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2016
• Number of pages: Str. 325-332
• Numbering: Vol. 17, iss. 6
• PID: 20.500.12556/RUL-111102
• UDC: 517.956.2
• ISSN on article: 1565-1339
• DOI: 10.1515/ijnsns-2016-0006
• COBISS.SI-ID: 17787993
• Publication date in RUL: 24.09.2019

Record is a part of a journal

• Title: International journal of nonlinear sciences and numerical simulation
• Shortened title: Int. j. nonlinear sci. numer. simul.
• Publisher: de Gruyter
• ISSN: 1565-1339
• COBISS.SI-ID: 10340886