We prove the non-degeneracy for the critical Lane-Emden system (equation presented) 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.
Non-degeneracy for the critical lane-emden system / Frank, R. L.; Kim, S.; Pistoia, A.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 149:1(2021), pp. 265-278. [10.1090/proc/15217]
Non-degeneracy for the critical lane-emden system
PISTOIA A.
2021
Abstract
We prove the non-degeneracy for the critical Lane-Emden system (equation presented) 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.File allegati a questo prodotto
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