Multiplicity solutions of a class fractional Schrödinger equations

Li-Jiang Jia; Bin Ge; Ying-Xin Cui; Liang-Liang Sun

Li-Jiang Jia ; Bin Ge ; Ying-Xin Cui ; Liang-Liang Sun

Open Mathematics, Tome 15 (2017), p. 1010-1023 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we study the existence of nontrivial solutions to a class fractional Schrödinger equations (−Δ)su+V(x)u=λf(x,u)inRN, ${(- Δ)}^{s} u + V (x) u = λ f (x, u) in ℝ^{N},$ where [...] (−Δ)su(x)=2limε→0∫RN∖Bε(X)u(x)−u(y)|x−y|N+2sdy,x∈RN ${(- Δ)}^{s} u (x) = 2 lim_{ε \to 0} \int_{ℝ^{N} ∖ B_{ε} (X)} \frac{u (x) - u (y)}{| x - y |^{N + 2 s}} d y, x \in ℝ^{N}$ is a fractional operator and s ∈ (0, 1). By using variational methods, we prove this problem has at least two nontrivial solutions in a suitable weighted fractional Sobolev space.

Publié le : 2017-01-01
EUDML-ID : urn:eudml:doc:288528

@article{bwmeta1.element.doi-10_1515_math-2017-0084,
     author = {Li-Jiang Jia and Bin Ge and Ying-Xin Cui and Liang-Liang Sun},
     title = {Multiplicity solutions of a class fractional Schr\"odinger equations},
     journal = {Open Mathematics},
     volume = {15},
     year = {2017},
     pages = {1010-1023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0084}
}

Li-Jiang Jia; Bin Ge; Ying-Xin Cui; Liang-Liang Sun. Multiplicity solutions of a class fractional Schrödinger equations. Open Mathematics, Tome 15 (2017) pp. 1010-1023. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0084/