Geodesic
Boundary-value problems for the biharmonic equation with a linear parameter
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $W_2^1(\mathbb{R}\times (0,1))$.
Classification : 35J40
Keywords: biharmonic equation, isomorphism, boundary-value problem 
@article{EJDE_2002__2002__a164,
     author = {Yakubov, Yakov},
     title = {Boundary-value problems for the biharmonic equation with a linear parameter},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a164/}
}
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Yakubov, Yakov. Boundary-value problems for the biharmonic equation with a linear parameter. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a164/