I've grown jalapeno plants here in TN for many years now and believe me, they cannot get too much sun. Could be too much water, but it actual sounds like not enough water. OR...
Does the container it's planted in drain well? Jalapenoes need lots of water, but don't like to sit in it.
Perhaps move it to a planter with holes in the bottom that sits in a tray. Then water the tray and let the plant wick up whatever it needs. Also, don't be afraid to prune some of those wilting leaves, but not too many. Especially leaves that are near the bottom of the plant.
Just my $0.02. Hope it helps.