Electron. J. Diff. Eqns., Vol. 2002(2002), No. 58, pp. 1-13.

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

Yakov Yakubov

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.

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Yakov Yakubov
Raymond and Beverly Sackler Faculty of Exact Sciences
School of Mathematical Sciences, Tel-Aviv University
Ramat-Aviv 69978, Israel
e-mail: yakubov@post.tau.ac.il

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