Nonlocal elliptic problems with nonlinear argument transformations near the points of conjugation

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We consider elliptic equations of order 2m in a domain Gⁿ with nonlocal conditions that connect the values of the unknown function and its derivatives on (n-1)-dimensional submanifolds Υᵢ (where ᵢΥᵢ=∂ G) with the values on ωis(Υᵢ)⊂ G. Nonlocal elliptic problems in dihedral angles arise as model problems near the conjugation points g∈Υᵢ∩Υⱼ≠, i≠ j. We study the case where the transformations ωis correspond to nonlinear transformations in the model problems. It is proved that the operator of the problem remains Fredholm and its index does not change as we pass from linear argument transformations to nonlinear ones.