Abstract
The paper is devoted to obtaining the sufficient conditions for Fredholm property for the general boundary value problem of the second‐order linear integro‐differential equation. Here, the boundary conditions corresponding with the boundary value problem contain both nonlocal and global terms.
Highlights
As is known, the boundary value problems are studied in differential equations theory and related areas in mathematical physics with local boundary conditions for linear elliptic partial differential equations 1–4
The second relations obtained from 4.1 – 4.3, that is, the expressions corresponding for ξ ∈ Γ, are necessary conditions
As it was noted above, necessary conditions are obtained from relations 4.1 – 4.3
Summary
The boundary value problems are studied in differential equations theory and related areas in mathematical physics with local boundary conditions for linear elliptic partial differential equations 1–4. Boundary value problems for linear ordinary differential equations sharply are different from the same problems for linear partial differential equations. We remove the misunderstandings given above when passing from boundary value problems for an ordinary differential equation to the problems for partial 7–9. Taking into account the fact that for the obtained singular integral equations we are on the spectrum, these singularities cannot be regularized by standard methods 11, 12. Joining the obtained regular relations with the given boundary conditions, we get sufficient condition on Fredholm property for the stated problems
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