Solvability of linear boundary-value problems for ordinary high-order differential systems in the spaces of continuously differentiable functions
DOI:
https://doi.org/10.3842/umzh.v78i9-10.9803Keywords:
Inhomogeneous boundary-value problems, d-characteristics , Fredholm operator , Fredholm numbers , spaces of smooth functions, high-order ordinary differential equations, differential systemsAbstract
UDC 517.927
We study the character of solvability of linear boundary-value problems for systems of high-order ordinary differential equations with the most general boundary conditions in normed spaces of continuously differentiable functions on a finite closed interval. The boundary conditions are allowed to be overdetermined or underdetermined with respect to the differential system and may also contain derivatives of the unknown functions of the order higher than the order of the differential system. We prove that the analyzed problem is Fredholm, find the index and $d$-characteristics of its operator, and also prove the limit theorems for the sequences of characteristic matrices of the boundary-value problems under study and for the $d$-characteristics of the corresponding Fredholm operators.
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