[doing sth; see also: indicate, propose, recommend
This suggests that A can exist.
Lemma 3 suggests that we start by considering A1.
Some other problems suggest themselves in the topological setting.
This suggests a question: under what conditions is it true that......?
The above construction suggests investigating the solutions of......
The first of these was suggested by J. Serrin, who showed how to modify my earlier treatment of...... so as to obtain stronger results with no extra effort.