| Abstract: |
| By Sobolev embeddings on S^{N-1} and the scaling invariant of the solutions, we show Lane-Emden conjecture holds in a new region; and we prove Henon-Lane-Emden conjecture is true for space dimension N=3 .
We also show new results on some Schrodinger systems, such as symmetry and asymptotic behavior of ground state solutions; bifurcation and multiple existence of positive solutions; uniqueness and structure of positive solutions; symmetry breaking via Morse index. |
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