I wish to find a joint PDF $h(p,b) $or CDF $H(p,b)$, given the following expression:
$(1-L) r \int _0^r\int _0^{\frac{p}{1-L}}h(p,b)dbdp- r L \int _0^r\int _0^{\frac{p-r}{1-L}+\frac{r}{L}}h(p,b)dbdp=0,$
where $0<L<1/2$ and $1/2<L<1$ and $r>0$ is some constaant. I naively tried the simple
Solve[{Integrate[h[p, b], {p, 0, r}, {b, 0, (p/(1 - L))}] (1 - L) r - Integrate[h[p, b], {p, 0, r}, {b, 0, (1/(1 - L)) (p - r) + (r/L)}] L r == 0 }, h[p, b]]
and of course it "does not work" since I receive the following answer
{{h[p, b] -> 0}}.
This answer is surely incorrect. Ideally, I should get some joint probability distribution function of the two variables $p$ and $b$. Also note that probably there are two solutions: one for $0<L1/2$ and the other for $1/2<L<1$ (so $l=1/2$ is excluded).