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

• Main Author: Yakov Yakubov
• Format: Article
• Language: English
• Published: Texas State University 2002-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: Biharmonic equation; isomorphism; boundary-value problem.
• Online Access: http://ejde.math.txstate.edu/Volumes/2002/58/abstr.html

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 $L_2(mathbb{R}imes (0,1))$ and $W_2^1(mathbb{R}imes (0,1))$.