Schrödinger equations with concave and convex nonlinearities

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Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations (2016, unknown): “Several papers are devoted to these kinds of problems, we just quote a few, for example, see [2, 6, 21, 26], but the most general results obtained by new proof techniques appeared in [29].”
A nonhomogeneous elliptic problem involving critical growth in dimension two (2008, background): “It is also well known that assumption (V 2) implies that these embeddings are compact for all 1 q < ∞ (see [15,17]).”
On Clark's theorem and its applications to partially sublinear problems (2015, unknown): “3 generalizes the result even for the case of p = 2 in [14].”