Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems.

Vitaly Volpert (1) , Vitali Vougalter (2)

1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
2 Department of Mathematics [University of Toronto]

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.

Domaines: Equations aux dérivées partielles [math.AP]

Vitaly Volpert, Vitali Vougalter. Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems.. Analysis and Mathematical Physics, 2012, 2, pp.473-496. ⟨10.1007/s13324-012-0046-1⟩. ⟨hal-00753099⟩