General form recursive equations .1.

In this article the general form recursive equations (GFRE) are considered. A necessary and sufficient condition for these equations to have a solution in the family of partial recursive functions is found. We show that there exists such a GFRE that, in contrast with usual case, it has a non-computable solution but has no solution in the class P of partial recursive functions. The problem of solution existence to GFRE is shown to be Sigma(3)(0)-complete and Sigma(1)(1)-complete in the classes P and the class of total recursive functions respectively.