Electron. J. Diff. Eqns., Vol. 2006(2006), No. 100, pp. 1-24.

Different types of solvability conditions for differential operators

Sergey G. Kryzhevich, Vitaly A. Volpert

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.

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Sergey G. Kryzhevich
Mathematics Department, Saint Petersburg University
28, Universitetskiy pr., 198504 Petrodvoretz, Russia
email: kryzhevitz@rambler.ru
Vitaly A. Volpert
Institute of Mathematics, UMR 5208 CNRS
University Lyon 1, 69622 Villeurbanne, France
email: volpert@math.univ-lyon1.fr

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