Second order ODE; Dirichlet problem; variational method; critical point

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.

Keywords

• Second order ODE
• Dirichlet problem
• variational method
• critical point