  The effect of a varying pseudo-magnetic field, which falls as $1/x^2$, on a
two dimensional electron gas in graphene is investigated. By considering the
second order Dirac equation, we show that its correct general solution is that
which might present singular wavefunctions since such field induced by elastic
deformations diverges as $x\rightarrow0$. We show that only this consideration
yields the known relativistic Landau levels when we remove such elastic field.
We have observed that the zero Landau level fails to develop for certain values
of it. We then speculate about the consequences of these facts to the quantum
Hall effect on graphene. We also analyze the changes in the relativistic
cyclotron frequency. We hope our work being probed in these contexts, since
graphene has great potential for electronic applications.
