Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity

Frank, Rupert L. und König, Tobias (2019): Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. In: Rendiconti Lincei-Matematica E Applicazioni, Bd. 30, Nr. 4: S. 817-846

Abstract

We consider positive solutions u of the semilinear biharmonic equation Delta(2)u = vertical bar x vertical bar(n+4/2) g(vertical bar x vertical bar(n-4/2)u) in R-n\{0} with non-removable singularities at the origin. Under natural assumptions on the nonlinearity g, we show that vertical bar x vertical bar(n-4/2)u is a periodic function of ln vertical bar x vertical bar and we classify all such solutions.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1120-6330
• Sprache: Englisch