Existence and uniqueness of mild solutions to stationary HJB equations in separable Hilbert spaces holds for any discount factor lambda > 0 via projected evolutionary lifting and maximally monotone operators.
Barbu,Nonlinear differential equations of monotone types in Banach spaces(Springer Monographs in Mathematics)
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Projected Evolutionary Lifting and Well-Posedness of Stationary Hamilton-Jacobi-Bellman Equations in Infinite Dimensions
Existence and uniqueness of mild solutions to stationary HJB equations in separable Hilbert spaces holds for any discount factor lambda > 0 via projected evolutionary lifting and maximally monotone operators.