Boundary-value problems for the biharmonic equation with a linear parameter

Wei Cheng Wang*, Yakov Yakubov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider two boundary-value problems for the equation Δ2u,(x,y) - λΔu(x,y) = f(x,y) with a linear parameter on a domain consisting of an infinite strip. These problems are not elliptic boundary-value problems with a parameter and therefore they are non-standard. We show that they are uniquely solvable in the corresponding Sobolev spaces and prove that their generalized resolvent decreases as 1/|λ| at infinity in L2(ℝ × (0, 1)) and W21 (R × (0, 1)).

Original languageEnglish
Pages (from-to)XCXIII-XCXIV
JournalElectronic Journal of Differential Equations
StatePublished - 2002


  • Biharmonic equation
  • Boundary-value problem
  • Isomorphism


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