Duffing equation and action functional Original Research Article

In this paper, we investigate the periodic nonlinear second order ordinary differential equation with friction View the MathML sourcex″(t)+cx′(t)+g(t,x(t))=f(t),t∈[0,T], Turn MathJax on View the MathML sourcex(0)=x(T),x′(0)=x′(T), Turn MathJax on where c∈Rc∈R, gg is a Caratheodory function, f∈L1(0,T)f∈L1(0,T), a quotient View the MathML sourceg(t,s)s lies between 00 and View the MathML sourcec24+(2πT)2 and a nonlinearity gg satisfies the potential Landesman–Lazer type condition. We introduce a corresponding energy functional and prove that its critical point is a classical solution to this problem.