Sign-changing and symmetry-breaking solutions to singular problems
2012 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 57, no 11, 1191-1208 p.Article in journal (Refereed) Published
We consider the degenerate elliptic equation -div(vertical bar x vertical bar(-ap) vertical bar del(u)vertical bar(p-2) del(u)) - lambda vertical bar x vertical bar(-p(a+1))vertical bar u vertical bar(p-2)u = vertical bar x vertical bar(-bq) vertical bar u vertical bar(q-2)u in R-N related to the Caffarelli-Kohn-Nirenberg inequality. We show that it possesses infinitely many solutions which are sign-changing and nonradial. The solutions are obtained by constrained minimization on subspaces consisting of functions which have certain prescribed symmetry properties. We also extend these results to higher order equations.
Place, publisher, year, edition, pages
2012. Vol. 57, no 11, 1191-1208 p.
concentration-compactness principle, degenerate elliptic equation, sign-changing solution, symmetry-breaking solution
IdentifiersURN: urn:nbn:se:su:diva-82978DOI: 10.1080/17476933.2010.504849ISI: 000310132900004OAI: oai:DiVA.org:su-82978DiVA: diva2:575189