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|Title: ||Strongly interacting bumps for the schrodinger-newton equations|
|Authors: ||Winter, M|
|Keywords: ||Schrodinger-Newton equations|
dimension of the kernel
|Publication Date: ||2009|
|Publisher: ||American Institute of Physics|
|Citation: ||Journal of Mathematical Physics. 50 (1)|
|Abstract: ||We study concentrated bound states of the Schrodinger-Newton equations
Moroz, Penrose and Tod proved the existence and
of ground states.
We first prove that the linearized operator around the unique ground state radial solution
has a kernel whose dimension is exactly 3 (correspondingto the translational modes).
Using this result we further show:
If for some positive integer K the points
P_i in R^3, i=1,2,...,K$ with P_i\not=P_j
for i\not=j are all local minimum or local maximum or nondegenerate critical points of the reduced energy function then forn h small enough
there exist solutions of the Schrodinger-Newton equations with K bumps which concentrate at P_i.
We also prove that given a local maximum point P_0 of the reduced energy there exists a solution with K bumps which all concentrate at P_0 and whose distances to P_0 are at least O(h^(1/3))|
|Appears in Collections:||Mathematical Science|
Dept of Mathematics Research Papers
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