Dear Werner,
Thank you very much for all your work and great explanations. I have been working on it for the last couple of days, and your help was very useful.
First of all thanks a lot for the reformulation of my code in the "first attempt", as you have noticed I am very new to this language, and it helped me a lot to learn.
It is true that I consider y as a fixed general parameter and you are totally right, that the first derivatives are the same and this simplifies the code. The conditions that pn must be a real positive is totally fine by assumption (and lambda different from one too).
For your second attempt, I think fixing pn and lambda in a first step should be a godd way to proceed even if it not working yet and I think I will continue on this way, 1) simplifying the problem (I will try to remove one equation by imposing p3=l3=0), 2) trying to show that this second system - where we replace lambda and pn afterwards is equivalent to the first one. I will certainly let you know here if this way I manage to solve it.
I also wanted to tell that one of the reasons I wanted to solve this problem was to find whether their actually is a solution (and I have the intuition there might not be).
Again, thanks a lot!
