Electron. J. Diff. Eqns., Vol. 2007(2007), No. 81, pp. 1-3.

Remark on Duffing equation with Dirichlet boundary condition

Petr Tomiczek

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.

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Petr Tomiczek
Department of Mathematics
University of West Bohemia
Univerzitni 22, 306 14 Plzen, Czech Republic
email: tomiczek@kma.zcu.cz

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