de Medeiros, Everaldo S.Cardoso, Jose Andersonde Souza, Manasses2022-04-042022-04-042017-03-20de Medeiros, E. S., Cardoso, J. A., & de Souza, M. (2017). Existence of standing waves for Schrodinger equations involving the fractional Laplacian. <i>Electronic Journal of Differential Equations, 2017</i>(76), pp. 1-10.1072-6691https://hdl.handle.net/10877/15603We study a class of fractional Schrödinger equations of the form ε2α(-∆)α u + V(x)u = ƒ(x, u) in ℝN, where ε is a positive parameter, 0 < α < 1, 2α < N, (-∆)α is the fractional Laplacian, V : ℝN → ℝ is a potential which may be bounded or unbounded and the nonlinearity ƒ : ℝN x ℝ → ℝ is superlinear and behaves like |u|p-2 u at infinity for some 2 < p < 2*α ≔ 2N / (N - 2α). Here we use a variational approach based on the Caffarelli and Silvestre's extension developed in [3] to obtain a nontrivial solution for ε sufficiently small.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalVariational methodsCritical pointsFractional LaplacianArticle