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Small perturbations of an indefinite elliptic equation
Author(s) -
Ramos Quoirin Humberto
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400353
Subject(s) - mathematics , perturbation (astronomy) , elliptic curve , mathematical analysis , argument (complex analysis) , physics , biochemistry , chemistry , quantum mechanics
We investigate a perturbed semilinear indefinite elliptic equation and show that the results known for the unperturbed equation still hold if the perturbation is sufficiently small. To this end, we use a continuity argument that allows us to establish the existence of two positive solutions even in the case where the strong maximum principle does not apply.