In the present work we study the multiplicity and concentration of positive solutions for the following class of Kirchhoff problems: −(ε2a+εb∫R3|∇u|2dx)Δu+V(x)u=f(u)+γu5in R3,u∈H1(R3),u>0in R3, where ε>0 is a small parameter, a,b>0 are constants, γ∈{0,1}, V is a continuous positive potential with a local minimum, and f is a superlinear continuous function with subcritical growth. The main results are obtained through suitable variational and topological arguments. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. Our theorems extend and improve in several directions the studies made in (Adv. Nonlinear Stud. 14 (2014), 483–510; J. Differ. Equ. 252 (2012), 1813–1834; J. Differ. Equ. 253 (2012), 2314–2351).

中文翻译：

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通过当地的山口通行证在一类基希霍夫问题上

在目前的工作中，我们研究以下类别的Kirchhoff问题的正解的多重性和集中性：R3中的-（ε2a+εb∫R3|∇u| 2dx）Δu+ V（x）u = f（u）+γu5， u∈H1（R3），u> 0在R3中，其中ε> 0是一个小参数，a，b> 0是常数，γ∈{0,1}，V是具有局部最小值的连续正电位，而f是具有亚临界增长的超线性连续函数。主要结果是通过适当的变分和拓扑论证获得的。通过将截断参数与Moser类型的迭代结合，我们还为上述问题的超临界版本提供了多重结果。我们的定理在（Adv.Nonlinear Stud.14（2014），483–510; J. Differ。Equ。252（2012），1813-1834; J. Differ.Equ.253（ 2012），2314–2351）。