Vitali Vougalter, Vitaly Volpert
Solvability in the sense of sequences for some non Fredholm operators with the bi-Laplacian
(130K, pdf)

ABSTRACT.  We study solvability of some linear nonhomogeneous elliptic problems and 
prove that under reasonable technical conditions the convergence in 
L^2(R^d) of their right sides implies the existence and the convergence 
in H^4(R^d) of the solutions. The equations involve the fourth order non Fredholm differential operators and we use the methods of spectral and scattering theory for Schrodinger type operators similarly to our preceding work [26].