Multiplicity solutions of a class fractional Schrödinger equations

Li-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 -