Geodesic
Exact multiplicity results for a \(p\)-Laplacian positone problem with concave-convex-concave nonlinearities
Electronic journal of differential equations, Tome 2004 (2004)
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 
@article{EJDE_2004__2004__a160,
     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},
     year = {2004},
     volume = {2004},
     zbl = {1057.34008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a160/}
}
TY  - JOUR
AU  - Addou,  Idris
AU  - Wang,  Shin-Hwa
TI  - Exact multiplicity results for a \(p\)-Laplacian positone problem with concave-convex-concave nonlinearities
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a160/
LA  - en
ID  - EJDE_2004__2004__a160
ER  - 
%0 Journal Article
%A Addou,  Idris
%A Wang,  Shin-Hwa
%T Exact multiplicity results for a \(p\)-Laplacian positone problem with concave-convex-concave nonlinearities
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a160/
%G en
%F EJDE_2004__2004__a160
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__a160/