Intrinsic Josephson effect and violation of the Josephson relation in layered superconductors

Equations describing the resistive state of a layered superconductor with anisotropic pairing are derived. The similarity with a stack of Josephson junctions is found at small voltages only, when current density in the direction perpendicular to the layers can be interpreted as a sum of the Josephson superconducting, the Ohmic dissipative, and the interference currents. In the spatially uniform state differential conductivity at higher voltages becomes negative. Nonuniformity of the current distribution generates branch imbalance and violates the Josephson relation between frequency and voltage.