Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems.
Résumé
We obtain solvability conditions in H2 for some elliptic equations in cylindrical domains using the methods of spectral theory and scattering theory for Schrödinger type operators. We prove the existence of standing solitary waves in H2 for some nonlinear equations. Both linear and nonlinear problems involve second order differential operators without Fredholm property.