Second order ODE; Dirichlet problem; variational method; critical point - Petr Tomiczek (Electronic Journal of Differential Equations, 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.