Geodesic
Sturm-Picone type theorems for second-order nonlinear differential equations
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\displaylines{ (p_1(t)|x'|^{\alpha-1}x')'+q_1(t)f_1(x)=0 \cr (p_2(t)|y'|^{\alpha-1}y')'+q_2(t)f_2(y)=0,\quad t_1}$$ in both regular and singular cases. Our results include some earlier results and generalize the well-known comparison theorems given by Sturm [19], Picone [18] and Leighton [5] which play a key role in the qualitative behaviour of the solutions.
Classification : 34C10, 34C15
Keywords: comparison theorem, Sturm-Picone theorem, half-linear, second order differential equations, singular equation, variational lemma 
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     author = {Tiryaki, Aydin},
     title = {Sturm-Picone type theorems for second-order nonlinear differential equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a3/}
}
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Tiryaki, Aydin. Sturm-Picone type theorems for second-order nonlinear differential equations. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a3/