Solvability conditions for some non-Fredholm operators

Vitali Vougalter (1) , Vitaly Volpert (2, 3)

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

We obtain solvability conditions for some elliptic equations involving non Fredholm operators with the methods of spectral theory and scattering theory for Schrödinger type operators. One of the main results of the work concerns solvability conditions for the equation −Delta u+V (x)u−au = f where a ≥ 0. They are formulated in terms of orthogonality of the function f to the solutions of the homogeneous adjoint equation.

Domaines: Equations aux dérivées partielles [math.AP]

Vitali Vougalter, Vitaly Volpert. Solvability conditions for some non-Fredholm operators. Proceedings of the Edinburgh Mathematical Society, 2011, 54 (1), pp.249-271. ⟨10.1017/S0013091509000236⟩. ⟨hal-00653658⟩