Nonlinear elliptic equations in dimension two with potentials which can vanish at infinity.
Author
Santaria Leuyacc, Yony Raúl
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.
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