# The String Equation in the F-theory Cosmology

We give an explicit expression for the F-theory string equations in the F-theory model. We show that, in the absence of gravity, the equations form essentially the same as in the Nielson-Frenkel-AdS black hole model, but obtain the corresponding solutions in the class of $R^2$-models. We also show that, in a subclass of $R^2$-models, the KK-model, the equations can be obtained from the solutions of the KK-model with respect to the $R^2$-models, and this class of models is also the "gold standard" for string equations in the F-theory model.