Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 81, pp. 1-3.

Title: Remark on Duffing equation  with Dirichlet boundary condition

Author: Petr Tomiczek (Univ. of West Bohemia, Czech Republic)

Abstract:
 In this note, we prove the existence of a solution to the
 semilinear second order ordinary differential equation
 $$\displaylines{
 u''(x)+ r(x) u'+g(x,u)=f(x)\,,\cr
 x(0)=x(\pi)=0\,,
 }$$
 using a variational method and critical point theory.
  
Submitted April 24, 2007. Published May 29, 2007.
Math Subject Classifications: 34G20, 35A15, 34K10.
Key Words: Second order ODE; Dirichlet problem; variational method;
           critical point.