Existence of three solutions to a double eigenvalue problem for the p-biharmonic equation

Lin Li; Shapour Heidarkhani

Annales Polonici Mathematici, Tome 105 (2012), p. 71-80 / Harvested from The Polish Digital Mathematics Library

Résumé

Using a three critical points theorem and variational methods, we study the existence of at least three weak solutions of the Navier problem ⎧ ${Δ (| Δ u |}^{p - 2} {Δ u) - d i v (| \nabla u |}^{p - 2} \nabla u) = λ f (x, u) + μ g (x, u)$ in Ω, ⎨ ⎩u = Δu = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ (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.

Publié le : 2012-01-01

Zbl 1248.35072

EUDML-ID : urn:eudml:doc:280859

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Lin Li; Shapour Heidarkhani. Existence of three solutions to a double eigenvalue problem for the p-biharmonic equation. Annales Polonici Mathematici, Tome 105 (2012) pp. 71-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-1-5/