gain public backing(That finding suggests that tougher measures to limit the gains on Wall Street, and executive pay, may be needed to gain public backing./BBC news Alex Krayevsky)
receive a boost(напр., об идее) Scientists suggested decades ago that water ice might be trapped in those shadowed areas at Mercury's poles. The idea received a boost in 1991, when the Arecibo radio telescope detected unusually radar-bright patches at Mercury's poles. I. Havkin)