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# Article

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Keywords:
half-linear equation; principal solution; limit characterization; integral characterization
Summary:
Some asymptotic properties of principal solutions of the half-linear differential equation $(a(t)\Phi (x^{\prime }))^{\prime }+b(t)\Phi (x)=0\,, \qquad \mathrm {(*)}$ $\Phi (u)=|u|^{p-2}u$, $p>1$, is the $p$-Laplacian operator, are considered. It is shown that principal solutions of (*) are, roughly speaking, the smallest solutions in a neighborhood of infinity, like in the linear case. Some integral characterizations of principal solutions of (), which completes previous results, are presented as well.
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