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We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials-(   p  ⁢   x  ′    )   ′   ⁢   (  t  )-   r  ⁢   (  t  )   ⁢  p  ⁢   (  t  )   ⁢   x  ′   ⁢   (  t  )+   q  ⁢   (  t  )   ⁢  x  ⁢   (  t  )=   f  ⁢   (  t  ,   x  ⁢   (  t  )    ){-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))}   , where the functionsp  ⁢   (  t  )    &gt;  0{p(t)&gt;0}   ,q  ⁢   (  t  ){q(t)}   ,r  ⁢   (  t  ){r(t)}    andf  ⁢   (  t  ,  x  ){f(t,x)}    are  2{\mathcal{C}^{2}}    and  T -periodic in the variable  t .

Periodic solutions for periodic second-order differential equations with variable potentials