Boundary-Value Problems for the Biharmonic Equation with a Linear Parameter
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We consider two boundary-value problems for the equation Δ2 u(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 x (0,1)) and W1 2 (ℝ x (0,1)).
CitationYakubov, Y. (2002). Boundary-value problems for the biharmonic equation with a linear parameter. Electronic Journal of Differential Equations, 2002(58), pp. 1-13.
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