Emden-Fowler type system: noether symmetries and first integrals

Abstract We classify a generalized coupled singular Emden-Fowler type system u + a ( t ) v n = 0, + b ( t ) u m = 0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits. First integrals of the various cases which admit Noether point symmetries are then obtained. This system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.