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.