Abstract
Existence of a positive, decaying radial solution to the problem
훥푢−푢+푢푝+휆푢푞=0 in ℝ푁,
when λ>0 and 1<q<p<(N+2)/(N−2) has been known for a long time. For λ=0, it is well known that this solution is unique. While uniqueness conditions for rather general non‐linearities have been found, the issue has remained elusive for this problem. We prove that uniqueness is in general not true. We find that if N=3, 1<q<3, λ is fixed sufficiently large, and p<5 is taken sufficiently close to 5, then there are at least three positive decaying radial solutions.
Original language | English |
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Pages (from-to) | 318-344 |
Journal | Proceedings of the London Mathematical Society |
Volume | 106 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Feb 2013 |