The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions

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On ground states for the Kirchhoff-type problem with a general critical nonlinearity (2015, result): “We refer to [10,34,11,38,12] for more existence results of (1.”
On double phase Kirchhoff problems with singular nonlinearity (2021, methodology): “This method has become a very powerful tool and has been used, for example, in the works of Chen-Kuo-Wu [9] (for degenerate Kirchhoff Laplacian problems with sign-changing weight), Fiscella-Mishra [22] (for fractional Kirchhoff problems), Kumar-Rădulescu-Sreenadh [32] (for critical (p, q)-equations)”
Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity (2015, background): “on a smooth bounded domain Ω ⊂ R and f : Ω × R → R a continuous function, has been extensively studied(see[1],[3],[10],[11],[15]-[20],[22],[23],[30]).”
Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, neutral): “For example, see [4,9–11,16,37,38].”
Multiple solutions for critical Choquard-Kirchhoff type equations (2020, methodology): “In [10] the authors prove existence and multiplicity of solutions by using the classical Nehari manifold method.”
Infinitely many sign-changing solutions for Kirchhoff type problems in R3 (2019, background): “By the Sobolev embedding theorem, for any r ∈ [2, 6], there exists C(r) > 0 such that ‖u‖r ≤ C(r)‖u‖E .”