Two solutions for a fourth order nonlocal problem with indefinite potentials

Multiplicity of solutions for the Kirchhoff equation with critical nonlinearity in high dimension

“…More recently, more and more authors began to pay attention to the higher dimensional problem when V(x) ≠ 0 (see previous studies [19][20][21][22][23] ). Sun et al 24 studied a class of superlinear Kirchhoff type equations with steep potential well and established the existence of two positive solutions by proposing new techniques and introducing new superlinear hypotheses on f. Li et al 25 considered the existence and nonexistence of energy minimizer of the Kirchhoff-Schrödinger energy function in dimension four.…”