I have a hard time finding the analytical solution to the following non-linear equation:
where and . I would like to have a solution in terms of for each fixed in the specified interval. Of course it's possible that no analytical form of the solution exists. If so, I'd also be happy to hear an argument why that is the case. However, for some values of p the solution is 'nice', for example for it's easy to compute that and for I obtained
Any kind of help is greatly appreciated!