Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 72, pp. 1-25.
Title: Exact multiplicity results for a p-Laplacian positone
problem with concave-convex-concave nonlinearities
Authors: Idris Addou (Univ. de Montreal, Canada)
Shin-Hwa Wang (National Tsing Hua Univ., Taiwan)
Abstract:
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 $p>1$, when the
nonlinearity satisfies $f(0)>0$ (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.