Geodesic
Exact multiplicity results for a $p$-Laplacian positone problem with concave-convex-concave nonlinearities
Electronic Journal of Differential Equations, Tome 2004 (2004).

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

Summary: We study the exact number of positive solutions of a two-point Dirichlet boundary-value problem involving the p-Laplacian operator. We consider the case $p=2$ and the case $p greater than 1$, when the nonlinearity satisfies $f(0) greater than 0$ (positone) and has three distinct simple positive zeros and such that $f''$ changes sign exactly twice on $(0,\infty)$. Note that we may allow $f''$ to change sign more than twice on $(0,\infty)$. We also present some interesting examples.
Classification : 34B18, 34B15
Keywords: exact multiplicity result, p-Laplacian, positone problem, bifurcation, concave-convex-concave nonlinearity, positive solution, dead core solution, time map 
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     author = {Addou, Idris and Wang, Shin-Hwa},
     title = {Exact multiplicity results for a $p${-Laplacian} positone problem with concave-convex-concave nonlinearities},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a60/}
}
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Addou, Idris; Wang, Shin-Hwa. Exact multiplicity results for a $p$-Laplacian positone problem with concave-convex-concave nonlinearities. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a60/