Fractional Schrödinger equations with new conditions

Date
2018-01-04
Authors
Benhassine, Abderrazek
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the nonlinear fractional Schrödinger equation (-∆)αu + V(x)u = ƒ(x, u) u ∈ Hα (ℝn, ℝ), where (-∆)α(α ∈ (0, 1)) stands for the fractional Laplacian of order α, x ∈ ℝn, V ∈ C(ℝn, ℝ) may change sign and ƒ is only locally defined near the origin with respect to u. Under some new assumptions on V and ƒ, we show that the above system has infinitely many solutions near the origin. Some examples are also given to illustrate our main theoretical result.
Description
Keywords
Fractional Schrödinger equations, Critical point theory, Symmetric mountain pass theorem
Citation
Benhassine, A. (2018). Fractional Schrödinger equations with new conditions. <i>Electronic Journal of Differential Equations, 2018</i>(05), pp. 1-12.