there exists variables satisfying an inequality

Hi,

Lets say we have a stability condition: ap^3+bp+c>0 (the real one is more complicated) and there exists a specific symbolic expresions/ values for a b & c such that the inequaility is true for all p. With the specific symbolic values of a,b,c obtained, the inequality would be satisfied provided an auxilliary (usually simpler) inequality is satisfied. I am particularly interested in these symbolic values of a,b,c and the auxilliary inequality.

Thanks