Boundary eigencurve problems involving the biharmonic operator

• Autorzy: Omar Chakrone , Najib Tsouli , Mostafa Rahmani , Omar Darhouche
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to study the spectrum of the fourth order eigenvalue boundary value problem
⎧Δ²u = αu + βΔu in Ω,
⎨
⎩u = Δu = 0 on ∂Ω.
where (α,β) ∈ ℝ². We prove the existence of a first nontrivial curve of this spectrum and we give its variational characterization. Moreover we prove some properties of this curve, e.g., continuity, convexity, and asymptotic behavior. As an application, we study the non-resonance of solutions below the first principal eigencurve of the biharmonic problem
⎧Δ²u = f(u,x) + βΔu + h in Ω,
⎨
⎩Δu = u = 0 ∂Ω, where f: Ω × ℝ → ℝ is a Carathéodory function and h is a given function in L²(Ω).

Kategorie tematyczne

• 35J40: Boundary value problems for higher-order elliptic equations
• 35J35: Variational methods for higher-order elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2014
• Tom: 41
• Numer: 2-3
• Strony: 267-275

Daty

wydano

2014

Twórcy

autor

Omar Chakrone

• Department of Mathematics, University Mohamed I, P.O. Box 717, Oujda 60000, Morocco

autor

Najib Tsouli

• Department of Mathematics, University Mohamed I, P.O. Box 717, Oujda 60000, Morocco

autor

Mostafa Rahmani

• Department of Mathematics, University Mohamed I, P.O. Box 717, Oujda 60000, Morocco

autor

Omar Darhouche

• Department of Mathematics, University Mohamed I, P.O. Box 717, Oujda 60000, Morocco

Identyfikatory

DOI

10.4064/am41-2-14