Multiplicity solutions of a class fractional Schrödinger equations

• Autorzy: Li-Jiang Jia , Bin Ge , Ying-Xin Cui , Liang-Liang Sun
• Języki publikacji: EN

Abstrakty

EN

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 \to 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.

Słowa kluczowe

EN

Fractional Laplacian; Variational methods; Nontrivial solution

Kategorie tematyczne

• 35P15: Estimation of eigenvalues, upper and lower bounds
• 35R11: Fractional partial differential equations
• 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1010-1023

Daty

wydano

2017-01-01

otrzymano

2016-11-08

zaakceptowano

2017-06-19

online

2017-08-08

Twórcy

autor

Li-Jiang Jia

• , , , ,

autor

Bin Ge

• , , , ,

autor

Ying-Xin Cui

• , , , ,

autor

Liang-Liang Sun

• , , , ,

Identyfikatory

DOI

10.1515/math-2017-0084