Nonnegative solutions of an indefinite sublinear Robin problem II: Local and global exactness results

Abstract

We proceed further in the investigation of the Robin problem (Pα) ⎧ ⎪⎪⎨ ⎪⎪⎩ −Δu = a(x)uq in Ω, u ≥ 0 in Ω, ∂νu = αu on ∂Ω, on a smooth bounded domain Ω ⊂ RN , with a sign-changing and 0 0. Moreover, strengthening the assumptions on a and q we provide a global (i.e., for every α > 0) exactness result on the number of solutions of (Pα) . Our approach also applies to the problem (Sα) ⎧ ⎪⎪⎨ ⎪⎪⎩ −Δu = αu + a(x)uq in Ω, u ≥ 0 in Ω, ∂ν u = 0 on ∂Ω.