The Ranges Of M-accretive And Monotone Operators' Noncompact Perturbation

Let X be a real Banach space with strictly convex dual space X* and G a bounded ,open subset of X. T : D(T) X→2X is a m-accretive operator,C : D(T)→ X is bounded operator. We study the solvability of 0 R(T + C) making use of condensing mappings'degree theorey.In the theorem 4,our boundary condition is only (I-(T + C))(D(T)G) G,In the circumstance, we study the solvability of 0 (T + C)(D(T) G) making use of L- S degree theory. The theorem omits another boundary condition (( T+ I)(D(T) G)) intG = 0 in the A.GKARTSATOS's paper , therefore, it extends A.GKARTSATOS's result.In the end, we consider the range of the sum of monotone and pseudo-monotone operators by using topological degree of operator of type (S+). In the proving, we mainly apply the theory that the sum of operators of pseudo-monotone and (S+) is still operator of type (S+).