An asymptotic formula for decreasing solutions to coupled nonlinear differential systems

An asymptotic formula is given for positive strongly decreasing solutions of a sub-homogeneous system of two second order quasilinear ordinary differential equations. This result is obtained as an application of an asymptotic equivalence theorem for positive solutions, which is proved in this paper as well. Examples of application to a fourth order nonlinear differential equation and to a nonlinear partial differential system are presented.