Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 21, pp. 1-27.

Title: Multiplicity of solutions for quasilinear elliptic boundary-value problems

Author: Idris Addou (USTHB, Institut de Mathematiques, Algerie)
         
Abstract: 
This paper is concerned with the existence of multiple solutions to the
boundary-value problem
  $$-(\varphi_p(u') ) '=\lambda \varphi_q(u) +f(u)\quad\hbox{in }
  (0,1)\,,\quad u(0) =u(1) =0\,,$$
where $p,q>1$,  $\varphi_x(y) =|y|^{x-2}y$, 
$\lambda $ is a real  parameter, and $f$ is a function which may be  
sublinear, superlinear, or asymmetric. 
We use the time map method for showing the existence of solutions. 

Submitted January 21, 1999. Published June 16, 1999. 
Math Subject Classification: 34B15.
Key Words:  Multiple solutions; elliptic boundary-value problems.