Ground states for Kirchhoff equations without compact condition

An autonomous Kirchhoff-type equation with general nonlinearity in RN

“…In the last ten years, by classical variational methods, there are many interesting results about the existence and nonexistence of solutions, sign-changing solutions, ground state solutions, the existence of positive solutions and positive ground states, least energy nodal solutions, multiplicity of solutions, semiclassical limit and concentrations of solutions to Kirchhoff type problems, see e.g. [3,4,5,11,12,13,20,25,26] and the references therein.…”

“…Many interesting results for the non-autonomous Problem (P) have been established for N = 1, 2, 3, see e.g. [11,13,25,26] and the references therein. By and large though, this question is still open, especially in the high dimensions case N ≥ 4.…”

Existence and multiplicity of solutions for a p-Kirchhoff equation on R N ${\mathbb {R}}^{N}$

“…Li and Ye [2] and Guo [3] showed the existence of a ground state solution for problem (1.2) with N = 3, where the potential V (x) ∈ C(R 3 ) and it satisfies V (x) ≤ lim inf |y|→+∞ V (y) V ∞ < +∞. Sun and Wu [4] investigated the existence and non-existence of nontrivial solutions with the following assumption: V (x) ≥ 0 and there exists c > 0 such that meas{x ∈ R N : V (x) < c} is nonempty and has finite measure.…”

Existence of nontrivial solutions for Schrödinger‐Kirchhoff type equations with critical or supercritical growth

“…The authors in Wang et al considered the multiplicity and concentration of positive solutions for a Kirchhoff‐type problem with critical growth. For more results, we refer the readers to the papers() and the references therein.…”

“…The authors in Wang et al 13 considered the multiplicity and concentration of positive solutions for a Kirchhoff-type problem with critical growth. For more results, we refer the readers to the papers [14][15][16][17][18] and the references therein. Most of those results need assume that the nonlinearity verifies subcritical or critical growth.…”