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 -