Abstract
In this note, we consider the following problem $$\displaystyle \begin {cases} -\Delta u=(1+g(x))u^{\frac {N+2}{N-2}},\ u>0\text{ in }B,\\ u=0\text{ on }\partial B, \end {cases} $$ where N ≥ 3 and \(B\subset \mathbb {R}^N\) is the unit ball centered at the origin and g(x) is a radial Hölder continuous function such that g(0) = 0. We prove the existence and nonexistence of radial solutions by the variational method with the concentration compactness analysis and the Pohozaev identity.KeywordsElliptic equationVariational methodCritical problem
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.