Global positive bounded solutions for equations with regularly varying operator

A nonlinear differential equation with inhomogeneous differential operator Φ which is regularly varying at zero, is considered. The operator Φ can be viewed as an extension of the p-Laplacian operator and arises in many physical problems, as illustrated by several examples. In particular, the existence of global positive bounded solutions on the half-line with the Neumann type boundary conditions is studied by means of an abstract fixed point theorem and certain properties of an associated half-linear equation. The results do not require the explicit form of the inverse operator of Φ, and are completed by an asymptotic analysis of these solutions near infinity.