【摘要】 该文考虑了下面的次临界的分数阶Choquard方程ε^2s（-Δ）^su+V（x）u=ε^μ-N(|x|^-μ*F（u）)f（u）,x∈R^N正解的存在性、多重性和集中现象,这里ε> 0是一个常数,s∈（0,1）,（-Δ）^s是分数阶Laplace算子,位势V:R^N→R是正的且有全局极小,0 <μ<min{4s,N},非线性项f∈C¹（R,R）是次临界增长的,F是f的原函数.该文的主要研究方法是变分法和Ljusternik-Schnirelmann理论.更多还原

【Abstract】 We are concerned with the existence,multiplicity and concentration of positive solutions for the following fractional Choquard equation with subcritical nonlinearityε^{2 s}（-△）^su+V（x）u=ε^μ-N（|x|-μ*F（u））f（u）,x∈R^N.where ε> 0 is a parameter,s ∈（0,1）,（-△）^s is the fractional Laplace operator,V:R^N→R is a positive potential having global minimum,0 <μ<min{4 s,N},and F is the primitive of f ∈ C¹（R,R） which is subcritical growth.The main research methods of this article are variational method and the Ljusternik-Schnirelmann theory.更多还原