PERTURBATIONS OF MONOTONE OPERATORS IN BANACH SPACES

Abstract

Various nonlinear equations of the types: Tx + Cx = f, Tx + Cx + Sx = f are studied. Results are obtained according to which the range of T + C contains a ball around zero. Other results guarantee that R(T + C) $\subset$ R(T + C + S) and int R(T + C) $\subset$ R(T + C + S).

The underlying space is a Banach space and the methods involve applications of the theories of degree and monotonicity.

Results of Browder, Reich, Kartsatos and other authors are thus extended.