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Positive solutions for an elliptic equation in an annulus with a superlinear nonlinearity with zeros
Author(s) -
Iturriaga Leonelo,
Massa Eugenio,
Sánchez Justino,
Ubilla Pedro
Publication year - 2014
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.201100285
Subject(s) - mathematics , multiplicity (mathematics) , nonlinear system , annulus (botany) , a priori and a posteriori , mathematical analysis , infinity , a priori estimate , elliptic curve , function (biology) , philosophy , botany , physics , epistemology , quantum mechanics , biology , evolutionary biology
We study existence, multiplicity, and the behavior, with respect to λ, of positive radially symmetric solutions of − Δ u = λ h ( x , u ) in annular domains inR N ,N ≥ 2 . The nonlinear term has a superlinear local growth at infinity, is nonnegative, and satisfies h ( x , a ( x ) ) = 0for a suitable positive and concave function a . For this, we combine several methods such as the sub and supersolutions method, a priori estimates and degree theory.