A variational formulation approach to a generalized coupled inhomogeneous Emden–Fowler system

Abstract

We study a generalized coupled inhomogeneous Emden–Fowler system from the Lagrangian formulation standpoint. A special case of this system was considered in the literature, and necessary and sufficient conditions for the existence of multiple positive solutions were obtained. Here we perform preliminary Noether classification of the generalized system by the direct method. We obtain nine cases for which the system has Noether point symmetries. First integrals are then obtained for the cases which admit Noether point symmetries.

Keywords:

• inhomogeneous Emden–Fowler system
• positive solution
• non-degeneracy
• Lagrangian
• Noether symmetry
• first integrals
• gauge function

AMS Subject Classifications:

• 34C14
• 34C20
• 34C40