Existence of three solutions for a class of (p₁,...,pₙ)-biharmonic systems with Navier boundary conditions

Shapour Heidarkhani; Yu Tian; Chun-Lei Tang

Shapour Heidarkhani ; Yu Tian ; Chun-Lei Tang

Annales Polonici Mathematici, Tome 105 (2012), p. 261-277 / Harvested from The Polish Digital Mathematics Library

Résumé

We establish the existence of at least three weak solutions for the (p1,…,pₙ)-biharmonic system ⎧ $Δ (| Δ u_{i} |^{p - 2} Δ u_{i}) = λ F_{u_{i}} (x, u ₁, \dots, u ₙ)$ in Ω, ⎨ ⎩ $u_{i} = Δ u_{i} = 0$ on ∂Ω, for 1 ≤ i ≤ n. The proof is based on a recent three critical points theorem.

Publié le : 2012-01-01

Zbl 1255.35103

EUDML-ID : urn:eudml:doc:280337

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     author = {Shapour Heidarkhani and Yu Tian and Chun-Lei Tang},
     title = {Existence of three solutions for a class of (p1,...,pn)-biharmonic systems with Navier boundary conditions},
     journal = {Annales Polonici Mathematici},
     volume = {105},
     year = {2012},
     pages = {261-277},
     zbl = {1255.35103},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-3-4}
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Shapour Heidarkhani; Yu Tian; Chun-Lei Tang. Existence of three solutions for a class of (p₁,...,pₙ)-biharmonic systems with Navier boundary conditions. Annales Polonici Mathematici, Tome 105 (2012) pp. 261-277. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-3-4/