【摘要】 本文考虑如下分数阶Kirchhoff方程:{M（∫∫R³×R³|u（x）-u（y）|²|x-y|3+2sdxdy）（-?）su（x）+V （x）u=f （u）, x∈R³,u∈H^s（R³）,其中M（t）=ε^2sa+ε^4s-3bt是Kirchhoff函数,3/4<s<1,ε>0是小参数,位势V是正连续函数且有全局极小,非线性项f连续且在无穷远处次临界增长.利用Ljusternik-Schnirelmann畴数理论,本文得到了正解个数与位势V全局极小集拓扑之间的关系,证明了当ε→0⁺时,这些正解在H^s（R³）中收敛到极限方程的基态解,且这些解集中在位势V的全局极小附近.此外也得到了解的衰减估计.更多还原

【Abstract】 In this paper, we consider the following fractional Kirchhoff equation,M(∫∫R³×R³|u（x）-u（y）|²|x-y|^3+2sdxdy)（-?）^su（x） + V（x）u = f（u）, in R³,u ∈ H^s（R³）,where M（t） = ε^2sa + ε^4s-3bt is a Kirchhoff function, 0 < s < 1 and ε > 0 is a small parameter, the potential V is a positive continuous function which has the global minimum, and f is supercubic but subcritical at infinity.Using the Ljusternik-Schnirelmann theory, we relate the number of positive solutions with the topology of the setΛ := {x ∈ R³: V（x） = inf V }, and we show that these positive solutions converge in H^s（R³） to a ground state solution of the limit equation, and concentrate around the set Λ in the sense that the values of V at the maximum points of these solutions convergent to the global minimum of V as ε → 0+. Moreover, the decay estimate of solutions is also established.更多还原