Abstract
We establish a nonlinear extension of the Poincaré–Perron theorem for a second order half-linear differential equation. Conditions are established which guarantee that all nontrivial solutions y of the equation are such that a proper limit limt→∞y′(t)∕y(t) exists. In addition, we discuss establishing precise asymptotic formulae for these solutions. We employ theory of regular variation and thereby, as a by-product, we complete some results for asymptotics of differential equations considered in this framework. The results can serve for comparison purposes involving more general equations and are of importance also from the stability point of view.
Published Version
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