Three Solutions for a Neumann Problem

  title={Three Solutions for a Neumann Problem},
  author={Biagio Ricceri},
In this paper we consider a Neumann problem of the type (Pλ) 8< : −∆u = α(x)(|u|q−2u− u) + λf(x, u) in Ω, ∂u ∂ν = 0 on ∂Ω. Applying the theory developed in [13], we establish, under suitable assumptions, the existence of an open interval Λ ⊆ R and of a positive real number %, such that, for each λ ∈ Λ, problem (Pλ) admits at least three weak solutions in W 1,2(Ω) whose norms are less than %. Let us recall that a Gâteaux differentiable functional J on a real Banach space X is said to satisfy the… CONTINUE READING

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