Sergey G. Kryzhevich, Vitaly A. Volpert
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.
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Sergey G. Kryzhevich Mathematics Department, Saint Petersburg University 28, Universitetskiy pr., 198504 Petrodvoretz, Russia email: kryzhevitz@rambler.ru |
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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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