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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.2 Antofagasta June 2019 


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

Yony Raúl Santaria Leuyacc1 

1Universidade de São Paulo Brasil e-mail :


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.

Keywords: Nonlinear elliptic equations; vanishing potentials; Trudinger-Moser inequality.

Texto completo disponible sólo en PDF.

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Received: October 2017; Accepted: March 2019

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