Geodesic
Conjugacy criteria for half-linear differential equations
Archivum mathematicum, Tome 35 (1999) no. 1, pp. 1-11 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Sufficient conditions on the function $c(t)$ ensuring that the half-linear second order differential equation \[ (|u^\prime |^{p-2} u^\prime )^\prime + c(t)|u(t)|^{p-2} u(t)=0\,, \quad \quad p>1 \] possesses a nontrivial solution having at least two zeros in a given interval are obtained. These conditions extend some recently proved conjugacy criteria for linear equations which correspond to the case $p=2$.
Sufficient conditions on the function $c(t)$ ensuring that the half-linear second order differential equation \[ (|u^\prime |^{p-2} u^\prime )^\prime + c(t)|u(t)|^{p-2} u(t)=0\,, \quad \quad p>1 \] possesses a nontrivial solution having at least two zeros in a given interval are obtained. These conditions extend some recently proved conjugacy criteria for linear equations which correspond to the case $p=2$.
Classification : 34C10
Keywords: half-linear equation; scalar p-Laplacian; conjugate points; conjugacy criteria 
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Peňa, Simón. Conjugacy criteria for half-linear differential equations. Archivum mathematicum, Tome 35 (1999) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/ARM_1999_35_1_a0/

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