Existence of three solutions to a double eigenvalue problem for the p-biharmonic equation
Lin Li, Shapour Heidarkhani (2012)
Annales Polonici Mathematici
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Using a three critical points theorem and variational methods, we study the existence of at least three weak solutions of the Navier problem ⎧ in Ω, ⎨ ⎩u = Δu = 0 on ∂Ω, where (N ≥ 1) is a non-empty bounded open set with a sufficiently smooth boundary ∂Ω, λ > 0, μ > 0 and f,g: Ω × ℝ → ℝ are two L¹-Carathéodory functions.