I have the following simultaneous equations:
\begin{aligned} &H(\lambda) = a\, \text{Li}_{3/2}\left(b\frac{H(\lambda)}{F(\lambda)}\right), \; \\&H(\lambda) = c\, \text{Li}_{3/2}\left(d \, \lambda \,{F(\lambda)}\right) \end{aligned}
where a,b,c,d are real positive numbers and $\text{Li}_{3/2}(z)$ is a Polylog function. I need to find $H({\lambda})$ and $F(\lambda)$ as functions of $\lambda$.
Any suggestions on how to proceed? Can we solve them atleast numerically if not analytically?