On compact perturbations of M-accretive and maximal monotone operators in Banach spaces

摘要

Let X be a real Banach space and G a bounded, open subset of X. The solvability of the problem the point s delong to (is member of) the set Tx + Cx, the point s delong to (is member of) the set X in D(T) intersect G_bar is considered, where T : X contains D(T) -> 2~X is m-accretive and C : D(T) -> X is either compact or is continuous with (T + I)~(-1) being compact, under the various assumptions of boundary conditions and coercivities which the operators T and C possess. Certain eigenvalue results are given involving the solvability of the point 0 delong to (is member of) the set Tx + #lambda#Cx with respect to the point (#lambda# , x) delong to (is member of) the set (0, infinity) * partial deriv G. Some analogous result on maximal monotone operators are also discussed in this paper.