Geodesic
Different types of solvability conditions for differential operators
Electronic journal of differential equations, Tome 2006 (2006)
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.
Classification : 34A30, 35J25, 47A53
Keywords: linear differential equations, solvability conditions, non-Fredholm operators 
@article{EJDE_2006__2006__a116,
     author = {Kryzhevich,  Sergey G. and Volpert,  Vitaly A.},
     title = {Different types of solvability conditions for differential operators},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1118.34003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a116/}
}
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Kryzhevich,  Sergey G.; Volpert,  Vitaly A. Different types of solvability conditions for differential operators. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a116/