Bound states for semilinear Schrödinger equations with sign-changing potential

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New Super-quadratic Conditions on Ground State Solutions for Superlinear Schrödinger Equation (2014, unknown): “(SQ) was first introduced by Liu and Wang [12] and then was commonly used in recent papers, see [4, 5, 6, 8, 9, 13, 14, 16, 20, 18, 23].”
Non-Nehari manifold method for asymptotically periodic Schrödinger equations (2014, methodology): “Afterwards, condition (SQ) was also used in many papers, see [3, 6, 7, 10, 11, 15, 16, 14, 26, 29, 34, 35].”
Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential (2015, methodology): “In [16], Ding and Szulkin studied the existence and the number of decaying solutions of problem (C)λ when V may change sign, satisfies (V4) and (V6) There exists b > 0 such that the set { x ∈ RN : V (x) < b} is nonempty and has finite measure; and f is either asymptotically linear or superlinear (bu”
New conditions on nonlinearity for a periodic Schrödinger equation having zero as spectrum (2014, background): “There is a large literature on existence and multiplicity results, for example, [3,5–7,9–11,15–17,19–23,27,28,30,32,33].”
Existence and multiplicity of solutions for a class of fourth-order elliptic equations in R^N (2012, unknown): “1 ((See [15] or [16])).”