Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition

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Multiplicity of high energy solutions for superlinear Kirchhoff equations (2012, background): “Zhang and Perera [12], Mao and Zhang [13] obtained three solutions (a positive solution, a negative solution and a sign-changing solution) by the invariant sets of descent flow.”
Existence of a positive solution to Kirchhoff type problems without compactness conditions (2012, background): “2) have been considered, such as the superlinear case [12]; and asymptotical linear case [16].”
Multiplicity of solutions for a class of Kirchhoff type problems (2010, result): “In [ 14 ] Mao and Zhang obtained a similar result as [18].”
Existence of positive solutions to Kirchhoff type problems with zero mass (2014, neutral): “2) have been considered, such as the superlinear case [19]; and asymptotical linear case [24].”
Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, methodology): “In Zhang and Perera [46] and Mao and Zhang [38], the authors used minimax methods and invariant sets of descent flow to prove the existence of three solutions (a positive solution, a negative solution and a sign-changing solution) for (1.1).”