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In this paper we establish the existence of nontrivial solutions to $$\frac{\mathrm{d}}{\mathrm{d}t}{L}_{x^{\text{'}}}(t,x^{\text{'}}\left(t\right))+V_x(t,x\left(t\right))=0,x\left(0\right)=0=x\left(T\right),$$ with $V_x$ superlinear in $x$.