Equal values of trinomials revisited

A necessary and sufficient condition is given for an equation $ax^m+bx^n+c=dy^p+ey^q$ to have infinitely many rational solutions with a bounded denominator, under the assumption that $m>n>0$, $p>q>0$, $ab\ne0\ne de$ and either $m>p>2$, or $m=p>2$ and $n\geq$. In a previous paper there was an additional assumption $(m,n)=(p,q)=1$.