Abstract
In this paper, we investigate the fractional Schödinger equation involving a critical growth. By using the principle of concentration compactness and the variational method, we obtain some new existence results for the above equation, which improve the related results on this topic.
Highlights
1 Introduction This paper is concerned with the following fractional Schödinger equation involving a critical nonlinearity: (– )αu(x) + V (x)u(x) = f x, u(x) + λ u(x) 2∗α–2u(x), x ∈ RN, (1.1)
To the best of our knowledge, our work is the first attempt to use the principle of concentration compactness to study the existence and multiplicity of solutions for fractional Schödinger equation involving a critical nonlinearity as in (1.1)
We study a new form of fractional Schödinger equation involving a critical nonlinearity (1.1)
Summary
1 Introduction This paper is concerned with the following fractional Schödinger equation involving a critical nonlinearity: (– )αu(x) + V (x)u(x) = f x, u(x) + λ u(x) 2∗α–2u(x), x ∈ RN , (1.1) In the past few years, many works were devoted to establishing the existence and multiplicity of solutions of fractional Schödinger equation, see [15,16,17,18,19,20,21,22] and the references therein. The existence of solutions of fractional Schödinger equation with perturbation was investigated, see [18,19,20,21].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
