Vitali Vougalter, Vitaly Volpert
Solvability conditions for some linear and nonlinear non-Fredholm 
elliptic problems
(230K, pdf)

ABSTRACT.  We obtain solvability conditions in H^2 for some elliptic equations in 
cylindrical domains using the methods of spectral theory and scattering 
theory for Schroedinger type operators. We prove the existence of standing solitary waves in H^2 for some nonlinear equations. Both linear 
and nonlinear problems involve second order differential operators without Fredholm property.