Geodesic
Asymptotic behavior of positive solutions for the radial $p$-Laplacian equation
Electronic Journal of Differential Equations, Tome 2012 (2012).

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

Summary: We study the existence, uniqueness and asymptotic behavior of positive solutions to the nonlinear problem $$\displaylines{ \frac{1}{A}(A\Phi _p(u'))'+q(x)u^{\alpha}=0,\quad \hbox{in }(0,1),\cr \lim_{x\to 0}A\Phi _p(u')(x)=0,\quad u(1)=0, }$$ where $$ \frac{1}{c}\leq q(x)(1-x)^{\beta }\exp \Big( -\int_{1-x}^{\eta }\frac{z(s)}{s}ds\Big)\leq c. $$ Our arguments combine monotonicity methods with Karamata regular variation theory.
Classification : 34B15, 35J65
Keywords: p-Laplacian, asymptotic behavior, positive solutions, Schauder's fixed point theorem 
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     author = {Ben Othman, Sonia and Maagli, Habib},
     title = {Asymptotic behavior of positive solutions for the radial $p${-Laplacian} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a5/}
}
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Ben Othman, Sonia; Maagli, Habib. Asymptotic behavior of positive solutions for the radial $p$-Laplacian equation. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a5/