Multiplicity of positive solutions of a nonlinear Schrödinger equation

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Solutions of perturbed Schrödinger equations with critical nonlinearity (2007, unknown): “[2,8] and their references.”
Multi-bump solutions for Choquard equation with deepening potential well (2015, methodology): “part, for Γ = {1,··· ,l}, with l ≤ k, it is easy to see that Z ΩΓ Z ΩΓ |u|p |x −y|µ dy |u|pdx 6= Xl i=1 Z Ωi Z Ωi |u|p |x −y|µ dy |u|pdx. And so it is impossible to repeat the same arguments in [15] to use the least energy solution of −∆u+u = Z Ωj |u|p |x −y|µ dy |u|p−2u, in Ω j, u 6= 0 , in”
Global Branch of Solutions for Non‐Linear Schrödinger Equations with Deepening Potential Well (2006, background): “See also [4, 6, 11] for further interesting developments in this direction.”