Published October 16, 2020
| Submitted
Journal Article
Open
Non-degeneracy for the critical Lane–Emden system
Abstract
We prove the non-degeneracy for the critical Lane–Emden system −ΔU = V^p, −ΔV = 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.
Additional Information
© 2020 by the authors. Received by the editors September 22, 2019, and, in revised form, May 17, 2020. The first author was partially supported by US National Science Foundation grant DMS-1363432. The second author was partially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF2017R1C1B5076384). The third author was partially supported by Fondi di Ateneo "Sapienza" Università di Roma (Italy). The authors appreciate the valuable comments and suggestions of two anonymous referees on an earlier version of this paper.Attached Files
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Additional details
- Eprint ID
- 107492
- Resolver ID
- CaltechAUTHORS:20210114-143038456
- DMS-1363432
- NSF
- NRF2017R1C1B5076384
- National Research Foundation of Korea
- Fondi di Ateneo "Sapienza" Università di Roma
- Created
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2021-01-15Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field