Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 52, pp. 1-42.

Title: Multiplicity results for classes of one-dimensional p-Laplacian
       boundary-value problems with cubic-like nonlinearities

Author: Idris Addou (USTHB Institut de Mathematiques, Alger, Algerie)
         
Abstract: 
 We study boundary-value problems of the type
 $$\displaylines{
 -(\varphi_{p}( u') ) ' =\lambda f( u) ,\hbox{ in }(0,1)  \cr
 u( 0)  =u( 1) =0,
 }$$
 where $p>1$, $\varphi_{p}( x) =\left| x\right| ^{p-2}x$, and
 $\lambda >0$. We provide multiplicity results when $f$ behaves like
 a cubic with three distinct roots, at which it satisfies Lipschitz-type
 conditions involving a parameter $q>1$. We shall show how changes in the
 position of $q$ with respect to $p$ lead to different behavior of the
 solution set. When dealing with sign-changing solutions, we assume
 that $f$ is {\it half-odd}; a condition generalizing the usual oddness.
 We use a quadrature method.
  
Submitted April 16, 1999. Revised May 1, 2000. Published July 3, 2000.
Math Subject Classifications: 34B15.
Key Words: p-Laplacian; time-maps; multiplicity results; 
           cubic-like nonlinearities.