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Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity

Djairo Guedes de FigueiredoJean-Pierre GossezPedro Ubilla — 2006

Journal of the European Mathematical Society

We study the existence, nonexistence and multiplicity of positive solutions for the family of problems Δ u = f λ ( x , u ) , u H 0 1 ( Ω ) , where Ω is a bounded domain in N , N 3 and λ > 0 is a parameter. The results include the well-known nonlinearities of the Ambrosetti–Brezis–Cerami type in a more general form, namely λ a ( x ) u q + b ( x ) u p , where 0 q < 1 < p 2 * 1 . The coefficient a ( x ) is assumed to be nonnegative but b ( x ) is allowed to change sign, even in the critical case. The notions of local superlinearity and local sublinearity introduced in [9] are essential in this...

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