поощрять

1) General subject: abet (чему-л. дурному), cheer, chuff, countenance, embolden, encourage, foster, give encouragement to (что-л.), imbolden, impregnate, incentify, incite into, incite to, promote, stimulate, uphold, incite, pat on the back, prime the pump, put a premium on, put a premium on (что-л.), aid and abet (кого-л. сделать что-л.), advocate, lend one's support to, nurture, advance, push for, turn thumbs up

2) Computers: encouraged

3) Colloquial: chuff up

4) American: favor, root, (for) rootle

5) Latin: incinere

6) Mathematics: excite

7) Economy: reward

8) Australian slang: pat (smb.) on the back, spark

9) Automobile industry: spur

10) Diplomatic term: cultivate

11) Business: favour

12) leg.N.P. patronize

13) Makarov: give encouragement to (smth.) (что-л.), nurse, pat on the back (кого-л.), soothe

14) Phraseological unit: cheer on (to barrack, to root for.), drum up, egg somebody on