ARAÚJO, Y. L. R.; http://lattes.cnpq.br/6642941380570085; ARAÚJO, Yane Lísley Ramos.
Résumé:
In this work we prove some results of existence and multiplicity of solutions for equations of the type (-Δ)αu + V(x)u = f(x; u) and ℝN, where 0 < α < 1, N ≥ 2α, (-Δ) denotes the fractional Laplacian, V : ℝN -> ℝ is a continuous function that satisfy suitable conditions and f:ℝNxℝ-> ℝ is a continuous function that may have critical growth in the sense of the Trudinger-Moser inequality or in the sense of the critical Sobolev exponent. In order to obtain our results we use variational methods combined with a version of the Concentration-Compactness Principle due to Lions.