NON-DEGENERACY FOR THE CRITICAL LANE-EMDEN SYSTEM

Frank, Rupert L. ; Kim, Seunghyeok and Pistoia, Angela (2021): NON-DEGENERACY FOR THE CRITICAL LANE-EMDEN SYSTEM. In: Proceedings of the American Mathematical Society, Vol. 149, No. 1: pp. 265-278

Abstract

We prove the non-degeneracy for the critical Lane-Emden system -Delta U = V-p, -Delta V = U-q, U, V > 0 in R-N for all N >= 3 and p, q > 0 such that 1/p+1 + 1/q+1 = N-2/N. We show that all solutions to the linearized system around a ground state must arise from the symmetries of the critical Lane-Emden system provided that they belong to the corresponding energy space or they tend to zero at infinity.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0002-9939
• Language: English