This is the question I mentioned previously. If $V$ is a separable,reflexive Banach space and $V^{*}$ it's dual space.
If $A:V \rightarrow V^{*}$ is pseudomonotone which means that $A$ is bounded and
whenever $u_{k} \rightharpoonup u$ and $\limsup\langle A(u_{k}), u_{k}-u \rangle \leq 0$ $\implies$ $\langle A(u),u-v \rangle \leq \liminf\limits_{k \rightarrow \infty} \langle A(u_{k}), u_{k} - v \rangle$ $\forall v \in V$ and it is coercive which means $\exists \zeta: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ such that $\lim_{s \rightarrow +\infty}$ and $\langle A(u),u \rangle \geq \zeta(\Ve…