Variational approach to a periodic problem with friction Original Research Article

Amster [P. Amster, Nonlinearities in a second order ODE, Electron. J. Differential Equations, Conf. 06 (2001) 13–21] found sufficient conditions for the existence of periodic solution to the second order ordinary differential equation View the MathML sourceu″(x)+r(x)u′(x)+g(x,u(x))=f(x), Turn MathJax on View the MathML sourceu(0)=u(T),u′(0)=u′(T). Turn MathJax on In this article, we generalize growth condition on gg and don’t suppose that rr is nondecreasing. The techniques we use are variational method and critical point theory.