Geodesic
Remark on Duffing equation with Dirichlet boundary condition
Electronic journal of differential equations, Tome 2007 (2007)
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.
Classification : 34G20, 35A15, 34K10
Keywords: second order ODE, Dirichlet problem, variational method, critical point 
@article{EJDE_2007__2007__a168,
     author = {Tomiczek,  Petr},
     title = {Remark on {Duffing} equation with {Dirichlet} boundary condition},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1142.34314},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a168/}
}
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Tomiczek,  Petr. Remark on Duffing equation with Dirichlet boundary condition. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a168/