In this paper, let X be a real Banach space with dual space X* and duality mapping F. We will study the solvability of the equation Tx + Cx contains s, s belongs to X, where T:D(T)-->2^x is m-accretiveand C:D(T)-->X is either compact or is bounded with C(T+I)^(-1) beingcompact. The main method employs the Leray-Schauder degree theory in order to ensure the existence of solutions of the approximate problemsTx + Cx + (1/n)x contain s, n=1,2,.... If x_n is a solution of the previous equations and show that (1/n)x_n-->0 as n approximates to infinte, in particular {x_n} is bounded, then the range of the sum T+C is dense in X, under the assumptions of various boundary conditionsand coercivities which the operators T and C possess. Furthermore, we also find some sufficient conditions on T and C such that the range of the sum T+C is surjective on X. Some analogous results on maximal monotone operators are also discussed in this paper. In the last partof our work, we shall concern the existence of certain eigenvalue results is given by solving Tx + kCx contains 0 with respect to k is a positive number and x belongs to the boundary of G, where G is a bounded,open subset of X.