Local “superlinearity” and “sublinearity” for the p-Laplacian
- de Figueiredo, Djairo G.
- Gossez, Jean-Pierre
- Ubilla, Pedro
DOIAbstract
AbstractWe study the existence, nonexistence and multiplicity of positive solutions for a family of problems −Δpu=fλ(x,u), u∈W01,p(Ω), where Ω is a bounded domain in RN, N>p, and λ>0 is a parameter. The family we consider includes the well-known nonlinearities of Ambrosetti–Brezis–Cerami type in a more general form, namely λa(x)uq+b(x)ur, where 0⩽q<p−1<r⩽p∗−1. Here the coefficient a(x) is assumed to be nonnegative but b(x) is allowed to change sign, even in the critical case. Preliminary results of independent interest include the extension to the p-Laplacian context of the Brezis–Nirenberg result on local minimization in W01,p and C01, a C1,α estimate for equations of the form −Δpu=h(x,u) with h of critical growth, a strong comparison resu...
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