[Closed] NL10 SH, JJ in battle of blinds

Hand converted with online PokerStrategy.com hand converter:

Play hand

$0.05/$0.1 No-Limit Hold'em (5 handed)

Known players:
[tg]BB$10.00:///////;MP3$10.45:///////;CO$10.00:///////;BU$13.80:///////;SB(Hero)$10.00:///////;[/tg]
Stats (VPIP/PFR/AF/Hands)
BB - 18/11/0.4/64

Preflop: Hero is SB with J:c, J:d.
3 folds, Hero raises to $0.4, BB raises to $1.5, Hero raises to $5, BB raises to $10(All-In), Hero calls $5.00(All-In).

Flop: ($20.00) 5:s, T:d, 5:c (2 players)

Turn: ($20.00) 2:d (2 players)

River: ($20.00) K:h (2 players)

Final Pot: $20.00.

Hi,
This was at least the 3rd time in a row I raised vs this guy in SB vs BB (I had a hand every time, AJ at least). Looked like he decided to make a stand. Is it ok to get all the money in with JJ in a battle of the blinds? Folding to his 3bet seems to be too weak, calling OOP doesn't seem to be a good option, and 4betting equals pushing

Thanks!