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 $0=a**0$. 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 $1**2$.
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.