We will focus on the existence of nontrivial solutions to the following nonlinear elliptic equation -Δu + 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.
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© 2019, Proyecciones Journal of Mathematics.
- Nonlinear elliptic equations
- Trudinger- Moser inequality
- Vanishing potentials