Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 09, pp. 1-29.
Title: Boundary-value problems for the one-dimensional
p-Laplacian with even superlinearity
Authors: Idris Addou (USTHB, Institut de Mathematiques, Algerie)
Abdelhamid Benmezai (USTHB, Institut de Mathematiques, Algerie)
Abstract:
This paper is concerned with a study of the quasilinear problem
$$ \displaylines{
-(|u'|^{p-2}u')'= |u|^p-\lambda ,\quad\mbox{in } (0,1)\,, \cr
u(0) =u(1) =0\,, \cr}
$$
where $p>1$ and $\lambda \in {\mathbb R}$ are parameters.
For $\lambda >0$, we determine a lower bound for the number of solutions
and establish their nodal properties.
For $\lambda \leq 0$, we determine the exact number of solutions.
In both cases we use a quadrature method.
Submitted October 28, 1998. Published March 8, 1999.
Math Subject Classification: 34B15, 34C10.
Key Words: One-dimensional p-Laplacian; two-point
boundary-value problem; superlinear; time mapping.