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Consider in a real Hilbert space H the differential equation (inclusion) (E): p(t)u″(t)+q(t)u′(t)∈Au(t)+f(t) a.e. in (0,∞), with the condition (B): u(0)=x∈D(A)¯, where A:D(A)⊂H→H is a (possibly set-valued) maximal monotone operator whose range contains 0; p,q∈L∞(0,∞), with essinfp>0 and q+∈L1(0,∞). More than four decades ago, V. Barbu established the existence of a unique bounded solution to (E),...
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