On the Solvability of an Essentially Nonlinear Elliptic Differential Equation with Nonlocal Boundary Conditions

Sufficient conditions for the existence of a generalized solution to a nonlinear elliptic differential equation with nonlocal boundary conditions of Bitsadze–Samarskii type are proved. The strong ellipticity condition is used for an auxiliary differential-difference operator. Under the formulated conditions, the differential-difference operator is demicontinuous, coercive, and has a semibounded variation, so the general theory of pseudomonotone operators can be applied.