TY - JOUR

T1 - Boundary-value problems for the biharmonic equation with a linear parameter

AU - Wang, Wei Cheng

AU - Yakubov, Yakov

PY - 2002

Y1 - 2002

N2 - 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)).

AB - 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)).

KW - Biharmonic equation

KW - Boundary-value problem

KW - Isomorphism

UR - http://www.scopus.com/inward/record.url?scp=52449121834&partnerID=8YFLogxK

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AN - SCOPUS:52449121834

SN - 1072-6691

VL - 2002

SP - XCXIII-XCXIV

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -