Perturbations of regularizing maximal monotone operators
Copyright policy )Perturbations of regularizing maximal monotone operators
We consideru′(t)+Au(t)∋f(t), whereA is maximal monotone in a Hilbert spaceH. AssumeA is continuous or A=ϱφ or intD(A)≠∅ or dimH<∞. For suitably boundedf′s, it is shown that the solution mapf→u is continuous, even if thef′s are topologized much more weakly than usual. As a corollary we obtain the existence of solutions ofu′(t)+Au(t)∋B(u(t)), whereB is a compact mapping inH.
- Vanderbilt University United States
Hilbert space, Nonlinear differential equations in abstract spaces, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Semigroups of nonlinear operators, compact perturbation, dissipative operator, continuous dependence, maximal monotone operators, Monotone operators and generalizations, accretive operator
Hilbert space, Nonlinear differential equations in abstract spaces, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Semigroups of nonlinear operators, compact perturbation, dissipative operator, continuous dependence, maximal monotone operators, Monotone operators and generalizations, accretive operator
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