How do I find if there exists a unique solution?

[johndcny]

Here is a set of linear and nonlinear equations:
sum{k from 1 to N}(N-k)R_k=D (D is a constant known)
sum{k from 1 to N}R_k=A (A is a constant known)
sum{k from 1 to N}P_k=E (E is a constant known) and
R_k=log(1+P_k) and P_k{greater than or equal to zero}

Does there exist a unique solution. I do not need to find the solution, I just need to show that a unique solution exist.

 

[johndcny]

By the way, even if you do not know the answer, it will be great if you can suggest me a source preferably available online. Thanks.