This isn't a very precisely worded question, but here goes:
Is there a sense in which generic smooth functions in $L^2$ will have multiple maxima?
Do arbitrary smooth functions in $L^2$ almost always have an arbitrarily large number of maxima?
These seems intuitively true to me, but I have no idea how I would go about showing them, or really even in what sense of genericity they are true. Are there additional/other nontrivial constraints I could impose on the function to make these statements true/easier to show?