Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 100, pp. 1-24.

Title: Different types of solvability conditions
       for differential operators

Authors: Sergey G. Kryzhevich (Saint Petersburg Univ., Russia)
         Vitaly A. Volpert (Univ. Lyon 1, France)

Abstract: 
  Solvability conditions for linear differential equations
  are usually formulated in terms of orthogonality of the right-hand side
  to solutions of the homogeneous adjoint equation.
  However, if the corresponding operator does not satisfy the
  Fredholm property   such solvability conditions may be not applicable.
  For this case, we obtain another type of solvability conditions,
  for ordinary differential equations on the real axis,
  and for elliptic problems in unbounded cylinders.

Submitted January 9, 2006. Published August 31, 2006.
Math Subject Classifications: 34A30, 35J25, 47A53.
Key Words: Linear differential equations; solvability conditions;
           non-Fredholm operators.