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)).
|Journal||Electronic Journal of Differential Equations|
|State||Published - 2002|
- Biharmonic equation
- Boundary-value problem