Fractional Schrödinger equations with new conditions
Texas State University, Department of Mathematics
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.
Fractional Schrödinger equations, Critical point theory, Symmetric mountain pass theorem
Benhassine, A. (2018). Fractional Schrödinger equations with new conditions. <i>Electronic Journal of Differential Equations, 2018</i>(05), pp. 1-12.