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On Semilinear Elliptic Equations Involving Concave and Convex Nonlinearities
Author(s) -
Chabrowski J.,
Bezzera do Ó João Marcos
Publication year - 2002
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 - 10.1002/1522-2616(200201)233:1<55::aid-mana55>3.0.co;2-r
Subject(s) - mathematics , regular polygon , concave function , mathematical analysis , pure mathematics , geometry
We prove some existence results for the problem (1 λ,μ ) with 0 < q < 1 < p depending on the range of parameters λ and μ. To establish the existence of solutions we use the method of successive approximations and the monotone method of sub and supersolutions. The cases where (i) a( x ) is bounded from below by a positive constant and (ii) a( x ) is bounded below by a positive constant outside a ball are considered. We also discuss the case where μ = 0 and λ is replaced by a positive or negative function. In this situation we use the variational method based on a constrained minimization combined with concentration‐compactness principle at infinity.