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dc.contributor.authorWinter, M-
dc.contributor.authorWei, J-
dc.identifier.citationJournal of Mathematical Physics. 50 (1)en
dc.description.abstractWe study concentrated bound states of the Schrodinger-Newton equations Moroz, Penrose and Tod proved the existence and uniqueness 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))en
dc.format.extent297234 bytes-
dc.publisherAmerican Institute of Physicsen
dc.subjectSchrodinger-Newton equationsen
dc.subjectstrong interactionen
dc.subjectsemi-classical limiten
dc.subjectdimension of the kernelen
dc.subjectmulti-bump statesen
dc.subjectLiapunov-Schmidt reductionen
dc.titleStrongly interacting bumps for the schrodinger-newton equationsen
dc.typeResearch Paperen
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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