Geodesic
The Application of Picone-type Identity for some Nonlinear Elliptic Differential Equations
Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 1 
G. Bognar; O. Dosly. The Application of Picone-type Identity
for some Nonlinear Elliptic Differential Equations. Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a3/
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     author = {G. Bognar and O. Dosly},
     title = {The {Application} of {Picone-type} {Identity
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     journal = {Acta mathematica Universitatis Comenianae},
     year = {2003},
     volume = {72},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

We established a Picone-type identity for the second order partial differential equation $$ \sum_{i=1}^N\frac{\partial}{\partial x_i} \left(r_i(x)\varphi\left(\frac{\partial u}{\partial x_i}\right)\right)+ c(x)\varphi(u)=0,\quad \varphi(u):=|u|^{p-1}u,\ p>0. \leqno{(*)} $$ Using this identity we prove the Leighton-type comparison theorem for a pair of equations of the form (*). Properties of the principal eigenvale of a certain eigenvalue problem associated with (*) are investigated as well.