Variational properties of solutions to linear equations in Banach space (Q2719448)

Let \(Y\) be a reflective Banach space, \( L:= \frac{d}{dt}-A\), where \(A\) is a constant unbounded closed operator in the Banach space with the domain of definition Dom\((A)\subset Y\). For the nonhomogeneous linear equation \( Ly(t) = g(t)\), where \( g\:\mathbb{R}\to Y \) is a strictly continuous function, the variational properties of weak solutions are studied.