Geodesic
Nonnegativity of functionals corresponding to the second order half-linear differential equation
Archivum mathematicum, Tome 35 (1999) no. 2, pp. 155-164.

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In this paper we study extremal properties of functional associated with the half–linear second order differential equation E$_p$. Necessary and sufficient condition for nonnegativity of this functional is given in two special cases: the first case is when both points are regular and the second is the case, when one end point is singular. The obtained results extend the theory of quadratic functionals.
Classification : 34C10, 49K15
Keywords: half–linear differential equation; associated functional; Picone identity; conjugate points 
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     author = {Ma\v{r}{\'\i}k, Robert},
     title = {Nonnegativity of functionals corresponding to the second order half-linear differential equation},
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Mařík, Robert. Nonnegativity of functionals corresponding to the second order half-linear differential equation. Archivum mathematicum, Tome 35 (1999) no. 2, pp. 155-164. http://geodesic.mathdoc.fr/item/ARM_1999__35_2_a7/