Electron. J. Diff. Eqns., Vol. 2004(2004), No. 137, pp. 1-14.

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

Xiao-Bao Shu, Yuan-Tong Xu

Abstract:
By means of variational structure and $Z_2$ group index theory, we obtain multiple solutions for the second-order differential equation
$$ \frac{d}{dt}(p(t)\frac{du}{dt})+q(t)u+f(t,u)=0 ,\quad 0 less than t less than 1, $$
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.

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Xiao-Bao Shu
Department of Mathematics
Sun Yat-Sen University
Guangzhou, 510275, China
email: sxb0221@163.com
Yuan-Tong Xu
Department of Mathematics
Sun Yat-Sen University
Guangzhou, 510275, China
email: xyt@zsu.edu.cn

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