Perturbations of M-accretive operators and quasi-linear evolution equations
Athanassios G. Kartsatos · Journal of the Mathematical Society of Japan · 1978
Let $X$ be a complex Banach space and let $A$ be an m-accretive operator with domain $D(A)\subseteqq X$ and range $R(A)\subseteqq X$ .Then a rather common problem in nonlinear perturbation theory is the following: given an accretive operator $B:D(B)\rightarrow X(D(B)\subseteqq D(A))$ , what additional assumptions on $B$ ensure the m- accretiveness of $A+B^{p}$ This problem can be rephrased as follows: let $U(v)u$ $=Au+Bv,$ $(u, v)\in D(A)\times D(A)$ .Assume thatU is m-accretive inuandaccretive in $v$ .