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Ground state solutions of non‐linear singular Schrödinger equations with lack of compactness
Author(s) -
Mihǎilescu Mihai,
Rǎdulescu Vicenţiu
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.403
Subject(s) - mathematics , compact space , sobolev space , mathematical proof , divergence (linguistics) , nirenberg and matthaei experiment , schrödinger equation , space (punctuation) , mathematical analysis , class (philosophy) , operator (biology) , type (biology) , schrödinger's cat , state (computer science) , ecology , philosophy , linguistics , biochemistry , geometry , chemistry , repressor , algorithm , artificial intelligence , biology , computer science , transcription factor , gene
We study a class of time‐independent non‐linear Schrödinger‐type equations on the whole space with a repulsive singular potential in the divergence operator and we establish the existence of non‐trivial standing wave solutions for this problem in an appropriate weighted Sobolev space. Such equations have been derived as models of several physical phenomena. Our proofs rely essentially on critical point theory tools combined with the Caffarelli–Kohn–Nirenberg inequality. Copyright © 2003 John Wiley & Sons, Ltd.