A degenerate Neumann problem for quasilinear elliptic integro-differentialoperators

This paper is devoted to the study of the following degenerate Neumann prob lem for a quasilinear elliptic integro-differential operator [GRAPHICS] Here W is a second-order elliptic integro-differential operator of Waldenfe ls type and Lu = a(x)partial derivative u/partial derivative v + b(x)u is a first-order Ventcel' operator with a(x) and b(x) being non-negative smooth functions on Gamma such that a(x) + b(x) > 0 on Gamma. Classical existence and uniqueness results in the framework of Holder spaces are derived under suitable regularity and structure conditions on the nonlinear term f(x, u, Du).