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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, $${(-\Delta )}^{s}u+V\left(x\right)u=\lambda f(x,u)\mathrm{in}{ℝ}^N,$$ where [...] (−Δ)su(x)=2limε→0∫RN∖Bε(X)u(x)−u(y)|x−y|N+2sdy,x∈RN ${(-\Delta )}^{s}u\left(x\right)=2\underset{\epsilon \to 0}{lim}{\int }_{{ℝ}^N\setminus B_{\epsilon }\left(X\right)}\frac{u\left(x\right)-u\left(y\right)}{|x-y{|}^{N+2s}}dy,x\in {ℝ}^N$ 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.

The packing constant is an important and interesting geometric parameter of Banach spaces. Inspired by the packing constant for Orlicz sequence spaces, the main purpose of this paper is calculating the Kottman constant and the packing constant of the Cesàro-Orlicz sequence spaces (${\mathrm{ces}}_{\phi }$) defined by an Orlicz function $\phi$ equipped with the Luxemburg norm. In order to compute the constants, the paper gives two formulas. On the base of these formulas one can easily obtain the packing constant for the Cesàro...