On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator

An essentially nonlinear equation containing the product of the $p$-Laplacian and a nonsymmetric difference operator is considered. Sufficient conditions guaranteeing the coercivity and pseudomonotonicity of the corresponding nonlinear difference-differential operator are obtained. The existence of a generalized solution of the Dirichlet problem for the nonlinear equation under consideration is proved.