Abstract
We examine the elliptic system given by1for 1 < p ⩽ θ and the fourth order scalar equation2where 1 < θ. We prove various Liouville type theorems for positive stable solutions. For instance we show there are no positive stable solutions of (1) (respectively, (2)) provided N ⩽ 10 and 2 ⩽ p ⩽ θ (respectively, N ⩽ 10 and 1 < θ). Results for higher dimensions are also obtained. These results regarding stable solutions on the full space imply various Liouville theorems for positive (possibly unstable) bounded solutions of3with u = v = 0 on . In particular there is no positive bounded solution of (3) for any 2 ⩽ p ⩽ θ if N ⩽ 11. Higher dimensional results are also obtained.
Sign-in/Register to access full text options 
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.
