Abstract: Let X be a real reflexive, strictly convex Banach space with its dual space X* being uniformly convex,T be a maximal monotone operator from D( T ) ??X to X
*, and C a continuous and bounded mapping from D( T ) ?? X toX* .Used by Leray- Schauder??s topology degree theory in nonlinear analysis, some new results are given to study the existence of solution of the operator equation ( T + C) x= f involving the maximal monotone operator T with the perturbation
C in an abstract space X .

Key words: monotone operator, compact mapping, duality mapping