On Fredholm Solvability and on the Index of the Generalized Neumann Problem for an Elliptic Equation of High Order on a Plane

In this paper, we investigate the Fredholm solvability of the generalized Neumann problem for a high-order elliptic equation on a plane. The equivalence of the solvability conditions of the generalized Neumann problem to the complementarity condition (Shapiro-Lopatinskii condition) is proved. The formula for the index of the specified problem in the class \(C^{2l,\mu }(\overline {D})\) is calculated.