Boundary-Value Problems for the Biharmonic Equation with a Linear Parameter
MetadataShow full metadata
We 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 W12 (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.
This work is licensed under a Creative Commons Attribution 4.0 International License.