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Multiplicity solutions of a class fractional Schrödinger equations

Li-Jiang JiaBin GeYing-Xin CuiLiang-Liang Sun — 2017

Open Mathematics

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 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 0 N B ε ( X ) u ( x ) - u ( y ) | x - y | N + 2 s d y , x 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.

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