Range Of Perturbed Maximal Monotone Operators In Banach Spaces

Let X is a real Banach space, T : D(T) E - 2X* is a maximal monotone operator, C : D(T) E - X* is a bounded operator (but not bound to continuous), while C(T + J)-1 is a compact operator. On the conditions of above, this paper studies the solvability of the following including relationships by adding certain boundary conditions and making use of Leray-Schauderdegree theory: 0 (T + C)(D(T) BQ(0)), 0 (T + C)(D(T) BQ(0))- andS R(T + C), intS intR(T + C)(where S X*); and B + D R(T + C), int(B + D)cintfl(T + C)(here B X*, D X*) ; Based on this, we derive some new conclusions.