Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 58, pp. 1-13.

Title: Boundary-value problems for the biharmonic equation with a
       linear parameter

Author: Yakov Yakubov (Tel-Aviv Univ., Israel)
         
Abstract: 
  We consider two boundary-value problems
  for the equation
  $$ \Delta^2 u(x,y)-\lambda \Delta u(x,y)=f(x,y) $$
  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 $1/|\lambda|$ at infinity
  in $L_2(\mathbb{R}\times (0,1))$ and $W_2^1(\mathbb{R}\times (0,1))$.
  
Submitted April 25, 2002. Published June 18, 2002
Math Subject Classifications: 35J40
Key Words: Biharmonic equation; isomorphism; boundary-value problem.