Geodesic
Limit and integral properties of principal solutions for half-linear differential equations
Archivum mathematicum, Tome 43 (2007) no. 1, pp. 75-86

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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.
Classification : 34C10, 34C11
Keywords: half-linear equation; principal solution; limit characterization; integral characterization 
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     title = {Limit and integral properties of principal solutions for half-linear differential equations},
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Cecchi, Mariella; Došlá, Zuzana; Marini, Mauro. Limit and integral properties of principal solutions for half-linear differential equations. Archivum mathematicum, Tome 43 (2007) no. 1, pp. 75-86. http://geodesic.mathdoc.fr/item/ARM_2007__43_1_a7/