encourage

[1]	hearten , embolden , reassure , buoy (up) , further , stimulate , animate , support , inspirit , inspire , cheer (up) , urge/spur on/onward(s) , incite , (Colloq) egg on , pep up
[2]	promote , advance , aid , support , help , assist , abet , foster , forward , boost , (Colloq) give a shot in the arm