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带有临界增长的分数阶Kirchhoff方程的半经典解
Semi-classical Solutions of Fractional Kirchhoff-type Equations with Critical Growth
本文研究如下带有临界增长的分数阶Kirchhoff方程ε2sM（ε2s-3 ∫∫R3×R3·(|u(x)?u(y)|2)/(|x-y|3+2s)dxdy）（-Δ）su+V（x）u=λW（x）f（u）+K（x）|u|2s*-2u，x ∈ R3，其中M是一个连续正的Kirchhoff函数，λ>0是一个参数，3/4<s<1，2s*：=6/（3-2s）是3维的临界指数，并且V（x），W（x）和K（x）都是正位势函数.在Kirchhoff函数M和位势函数的适当假设下，当ε>0充分小和λ足够大时，我们首先证明了上述问题正基态解的存在性.其次，证明了基态解集中在一个由位势函数所刻画的特定集合中.最后，研究了基态解的衰减估计.
In this paper, we study the following fractional Kirchhoff-type equation with critical growth ε2sM(ε2s-3 ∫∫R3×R3(|u(x)?u(y)|2)/(|x-y|3+2s)dxdy)(-Δ)su + V (x)u=λW(x)·f(u) + K(x)|u|2s*-2u, x ∈ R3, where M is a continuous and positive Kirchhoff function, λ > 0 is a parameter, (-Δ)s is the fractional Laplace operator with 3/4 < s < 1, V (x), W(x) and K(x) are all positive potentials. Under some assumptions on potentials, we obtain the existence of a positive ground state solution for ε > 0 small and λ large. Moreover, we show that these ground state solutions concentrate at a special set characterized by potentials. Finally, we study the decay estimate of ground state solutions.
分数阶Kirchhoff方程 / 临界增长 / 半经典基态解 / 集中 {{custom_keyword}} /
fractional Kirchhoff-type equation / critical growth / semiclassical ground states / concentrating {{custom_keyword}} /
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国家自然科学基金资助项目（11771385）
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