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, Vol. 30, No. 4: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1120-6330
• Language: English