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

摘要: We consider elliptic equations of order $2m$ in a domain $G\subset\mathbb R^n$ with nonlocal conditions that connect the values unknown function and its derivatives on $(n-1)$-dimensional submanifolds $\Upsilon_i$ (where $\bigcup_i\Upsilon_i=\partial G$) $\omega_{is}(\overline\Upsilon_i)\subset\overline G$. Nonlocal problems dihedral angles arise as model near conjugation points $g\in\overline\Upsilon_i\cap\Upsilon_j\ne\varnothing$, $i\ne j$. study case where transformations $\omega_{is}$ correspond to nonlinear problems. It is proved operator problem remains Fredholm index does not change we pass from linear argument ones.