# Multiplicity solutions of a class fractional Schrödinger equations

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

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1010-1023
- ISSN: 2391-5455

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topLi-Jiang Jia, et al. "Multiplicity solutions of a class fractional Schrödinger equations." Open Mathematics 15.1 (2017): 1010-1023. <http://eudml.org/doc/288528>.

@article{Li2017,

abstract = {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, \[ \{( - \Delta )^s\}u + V(x)u = \lambda f(x,u)\,\,\{\rm in\}\,\,\{\mathbb \{R\}^N\}, \]
where [...] (−Δ)su(x)=2limε→0∫RN∖Bε(X)u(x)−u(y)|x−y|N+2sdy,x∈RN $ \{( - \Delta )^s\}u(x) = 2\lim \limits _\{\varepsilon \rightarrow 0\} \int _ \{\{\mathbb \{R\}^N\}\backslash \{B_\varepsilon \}(X)\} \{\{u(x) - u(y)\} \over \{|x - y\{|^\{N + 2s\}\}\}\}dy,\,\,x \in \{\mathbb \{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.},

author = {Li-Jiang Jia, Bin Ge, Ying-Xin Cui, Liang-Liang Sun},

journal = {Open Mathematics},

keywords = {Fractional Laplacian; Variational methods; Nontrivial solution},

language = {eng},

number = {1},

pages = {1010-1023},

title = {Multiplicity solutions of a class fractional Schrödinger equations},

url = {http://eudml.org/doc/288528},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Li-Jiang Jia

AU - Bin Ge

AU - Ying-Xin Cui

AU - Liang-Liang Sun

TI - Multiplicity solutions of a class fractional Schrödinger equations

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1010

EP - 1023

AB - 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, \[ {( - \Delta )^s}u + V(x)u = \lambda f(x,u)\,\,{\rm in}\,\,{\mathbb {R}^N}, \]
where [...] (−Δ)su(x)=2limε→0∫RN∖Bε(X)u(x)−u(y)|x−y|N+2sdy,x∈RN $ {( - \Delta )^s}u(x) = 2\lim \limits _{\varepsilon \rightarrow 0} \int _ {{\mathbb {R}^N}\backslash {B_\varepsilon }(X)} {{u(x) - u(y)} \over {|x - y{|^{N + 2s}}}}dy,\,\,x \in {\mathbb {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.

LA - eng

KW - Fractional Laplacian; Variational methods; Nontrivial solution

UR - http://eudml.org/doc/288528

ER -

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