Ground state solutions of scalar field fractional Schrödinger equations

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On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent (2017, background): “The cited results turn out to be very fruitful in order to recover an elliptic PDE approach in a nonlocal framework, and they have recently been used very often, see [1, 2, 14, 17, 20, 21].”
Fractional double-phase patterns: concentration and multiplicity of solutions (2020, background): “We stress that, when p = q = 2, equation (3) boils down a fractional Schrödinger equation (see [51]) of the type ε2s(−Δ)su + V (x)u = f(x, u) in R , (4) which has been extensively considered by several authors; see [44,40,57,67].”
Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations (2016, background): “Models governedby the fractional p-Laplacian andunboundedpotentials are investigated in [5, 22, 32].”