Eggplant not setting fruit

Eggplant not setting fruit

I have one eggplant plant that I'm growing (first time ever trying this plant), and it's flowering like crazy, but not setting fruit. The flowers are very delicate, and if I touch one, it falls off. So I've been very careful around it. I water well (though not too much) and fertilize about once a week. The plant is very healthy looking, just not setting any eggplants. I have tomato plants, and my first tomato has started to ripen already. What am I doing wrong with the eggplant? Any ideas?
My Humble Abode

My Humble Abode

hello!

hello!

Can I get it to bush up?

Can I get it to bush up?

tomato bottoms turning black!  and bumps on the stem

tomato bottoms turning black! and bumps on the stem

Malabar spinach

Malabar spinach

A couple of funny zinnias

A couple of funny zinnias