Elliptic problem driven by different types of nonlinearities

Choudhuri, Debajyoti (author), Repovš, Dušan (author)

In this paper we establish the existence and multiplicity of nontrivial solutions to the following problem: $$(-\Delta )^{\frac{1}{2}}u+u+\bigl(\ln \vert \cdot \vert \ast \vert u \vert ^{2}\bigr) = f(u)+\mu \vert u \vert ^{- \gamma -1}u,\quad \text{in }\mathbb{R},$$ where $\mu > 0$, $(\ast)$ is the convolution operation between two functions, $0<\gamma <1$, $f$ is a function with a certain type of growth. We prove the existence of a nontrivial solution at a certain mountain pass level and another ground state solution when the nonlinearity $f$ is of exponential critical growth.

• Language: English
• Keywords: fractional Laplacian, ground state solution, singularity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: 19 str.
• Numbering: Vol. 2021, art. 85
• PID: 20.500.12556/RUL-132413
• UDC: 517.956
• ISSN on article: 1687-2770
• DOI: 10.1186/s13661-021-01562-1
• COBISS.SI-ID: 81756163
• Publication date in RUL: 25.10.2021

Record is a part of a journal

• Title: Boundary value problems
• Shortened title: Bound. value probl.
• Publisher: Springer
• ISSN: 1687-2770
• COBISS.SI-ID: 62113025

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.