Small perturbations of an indefinite elliptic equation

Small perturbations of an indefinite elliptic equation

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...

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Veröffentlicht in:Mathematische Nachrichten 2015-10, Vol.288 (14-15), p.1727-1740
1. Verfasser: Ramos Quoirin, Humberto
Format: Artikel
Sprache:eng
Schlagworte:
35J20
35J62
35J92
Indefinite elliptic problem
nonhomogeneous nonlinearity
variational methods
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Zusammenfassung: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201400353