Exactness Results for Generalized Ambrosetti-Brezis-Cerami Problem and Related One-dimensional Elliptic Equations
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-(φp(u'))' = φα(u) + λφβ(u) in (0,1)
u(0) = u(1) = 0
where φp(x) = |x|p-2 x, p, α, β > 1 and λ ∈ ℝ*. We give the exact number of solutions for all λ and most values of α, β, p > 1. In the particular case where 1 < β < p = 2 < α, we resolve completely a problem suggested by A. Ambrosetti, H. Brezis and G. Cerami and which was partially solved by S. Villegas.