Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 01, pp. 1-26.

Title: Exact multiplicity results for quasilinear boundary-value problems 
       with cubic-like nonlinearities

Author: Idris Addou (USTHB, Institut de Mathematiques, Alger, Algerie)

Abstract: 
We consider the boundary-value problem 
$$\displaylines{
-(\varphi_p (u'))' =\lambda f(u) \mbox{ in }(0,1) \cr
u(0) = u(1) =0\,,
}$$
where $p>1$, $\lambda >0$ and $\varphi_p (x) =| x|^{p-2}x$.
 The nonlinearity $f$ is cubic-like with three distinct roots $0=a<b<c$.
By means of a quadrature method, we provide the exact number of solutions
for all $\lambda >0$. This way we extend a recent result, for $p=2$, by
Korman et al. \cite{KormanLiOuyang} to the general case $p>1$.  We shall
prove that when $1<p\leq 2$ the structure of the solution set is exactly the
same as that studied in the case $p=2$ by Korman et al. \cite{KormanLiOuyang}, 
and strictly different in the case $p>2$.

An addendum to this article was attached on May 3, 2000. There it is shown that
Possibility B of Theorem 2.4  and  Possibility D of Theorem 2.5 never happen.

Submitted May 26, 1999. Revised October 1, 1999. Published January 1, 2000.
Math Subject Classifications: 34B15.
Key Words: One dimensional p-Laplacian; multiplicity results; time-maps.