# Nonlinear elliptic equations in dimension two with potentials which can vanish at infinity.

### Abstract

We will focus on the existence of nontrivial solutions to the following nonlinear elliptic equation −∆u + V (x)u = f(u), x ∈ R2, where V is a nonnegative function which can vanish at infinity or be unbounded from above, and f have exponential growth range. The proof involves a truncation argument combined with Mountain Pass Theorem and a Trudinger-Moser type inequality.### References

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