Yakubov, Yakov2020-08-112020-08-112002-06-18Yakubov, Y. (2002). Boundary-value problems for the biharmonic equation with a linear parameter. <i>Electronic Journal of Differential Equations, 2002</i>(58), pp. 1-13.1072-6691https://hdl.handle.net/10877/12360We consider two boundary-value problems for the equation Δ2 u(x, y) - λΔu(x, y) = ƒ(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)).Text13 pages1 file (.pdf)enAttribution 4.0 InternationalBiharmonic equationIsomorphismBoundary-value problemArticle