The question is from Avner Friedman's Variational Principles and Free-Boundary Problems. It goes:
Let $A: X \to X'$ be monotone, hemicontinuous, and continuous on finite dimensional subspaces of the domain $D(A)$ ($X$ is a reflexive Banach space, and $X'$ is its dual).
Then let $K$ be a closed, unbounded, convex subset of $X$.
Suppose there exists a $\phi_{o} \in K$ such that $(1 + \theta) \phi_{o} \in K$ for some $\theta > 0$. Show that the condition
$$ \frac{\langle Av,v\rangle }{|v|} \to \infty \; as \; |v| \to \infty $$
implies that
$$ \frac{\langle Av - A\phi_{o}, v - \phi_{o} \rangle}{|v|} \to \infty \; as \; |v| \to \infty $$
Any help with variational inequalities, free boundary problems, and nonlinear-functional analysis would also be helpful, such as books, web resources, lectures, etc.