Multiplicity of solutions for a perturbed fractional Schrödinger equation involving oscillatory terms
MetadataShow full metadata
In this article we study the perturbed fractional Schrödinger equation involving oscillatory terms
(-∆)αu + u = Q(x) (ƒ(u) + ɛg(u)), x ∈ ℝN
u ≥ 0,
where α ∈ (0, 1) and N > 2α, (-∆)α stands for the fractional Laplacian, Q : ℝN → ℝN is a radial, positive potential, ƒ ∈ C([0, ∞), ℝ) oscillates near the origin or at infinity and g ∈ C([0, ∞), ℝ) with g(0) = 0. By using the variational method and the principle of symmetric criticality for non-smooth Szulkin-type functionals, we establish that: (1) the unperturbed problem, i.e. with ε = 0 has infinitely many solutions; (2) the number of distinct solutions becomes greater and greater when |ε| is smaller and smaller. Moreover, various properties of the solutions are also described in terms of the L∞- and Hα (ℝN)-norms.
CitationJi, C., & Fang, F. (2018). Multiplicity of solutions for a perturbed fractional Schrödinger equation involving oscillatory terms. Electronic Journal of Differential Equations, 2018(126), pp. 1-21.
This work is licensed under a Creative Commons Attribution 4.0 International License.