Constructing PDA to accept language $L=\{a^i b^j c^k \mid k\geq \min(i,j)\}$
Your idea to differentiate between $i&lt;j$ and $i &gt;j$ is good.
To help you building the PDA, note that $L = \{a^ib^jc^k | k \geq i\} \cup \{a^ib^jc^k|k\geq j\}$.
I hope that hint is enough.