Electron. J. Diff. Eqns., Vol. 2004(2004), No. 72, pp. 1-25.

Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities

Idris Addou & Shin-Hwa Wang

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.

Submitted March 8, 2004. Published May 20, 2004.
Math Subject Classifications: 34B18, 34B15.
Key Words: Exact multiplicity result, p-Laplacian, positone problem, bifurcation, concave-convex-concave nonlinearity, positive solution, dead core solution, time map.

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Idris Addou
Departement de Mathematiques et Statistiques
Universite de Montreal
C.P. 6128, Succ. Centre-ville, Montreal, Quebec, Canada, H3C2J7
email: addou@dms.umontreal.ca
Shin-Hwa Wang
Department of Mathematics
National Tsing Hua University
Hsinchu, Taiwan 300, Republic of China
email: shwang@math.nthu.edu.tw

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