Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 137, pp. 1-14.

Title: Existence of multiple solutions for a class of second-order
       ordinary differential equations

Authors: Xiao-Bao Shu (Sun Yat-Sen Univ. Guangzhou, China)
         Yuan-Tong Xu (Sun Yat-Sen Univ. Guangzhou, China)

Abstract: 
 By means of variational structure and $Z_2$ group
 index theory, we obtain multiple solutions for the second-order
 differential equation
 $$ \frac{d}{dt}(p(t)\frac{du}{dt})+q(t)u+f(t,u)=0 ,\quad 0<t<1,
 $$
 subject to one of the following two sets of boundary conditions:
 $$
 u'(0) = u(1)+  u'(1)=0\quad\hbox{or}\quad u(0)=u(1)=0\,.
 $$

Submitted October 5, 2004. Published November 25, 2004.
Math Subject Classifications: 34B15, 34B05, 65K10, 34B24.
Key Words: Variational structure; $Z_2$ group index theory;
           critical points; boundary value problems.