Existence of standing waves for Schrodinger equations involving the fractional Laplacian
Date
2017-03-20
Authors
de Medeiros, Everaldo S.
Cardoso, Jose Anderson
de Souza, Manasses
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Variational methods, Critical points, Fractional Laplacian
Citation
de 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.
Rights
Attribution 4.0 International