题 目: Least energy solutions of fractional Schrod-
inger equations involving potential wells
摘要：In this talk, we study a class of nonlinear Schrodinger equations involving the fractional Laplacian. We assume that the potential of the equations includes a parameter. Moreover, the potential behaves like a potential well when the parameter is large. Using variational methods, combining Nehari methods, we prove that the equation has a least energy solution which, as the parameterlarge, localizes near the bottom of the potential well. Moreover, if the zero set int of V(x) includes more than one isolated component, then will be trapped around all the isolated components. However, in Laplacian case when s=1, for large, the corresponding least energy solution will be trapped around only one isolated component and will become arbitrary small in other components of int . This is the essential difference with the Laplacian problems since the operator fractional is nonlocal.