On evolution equations having monotonicities of opposite sign

Abstract

(whenever meaningful), that applied to two solutions of (l), by the monotonicity of A and the minus sign on the right hand side, yields that their distance is nonincreasing. This reasoning allows us the construction of a Cauchy sequence of approximate solutions, converging to a solution. The existence of the right approximate solutions is supplied by the maxi- mality of A, that permits the use of the Yosida approximations. Hence existence is a result of completeness, of having the sign minus at the right hand side, and of maximality. The same conditions have allowed to prove existence for several classes of perturbations of (1) to i(f)E -Ax(t)+F(t,x(t)) in [4, 2, 9, 10, 14, 13, 11, 12, 15, 171. 71