Higher-order subcritical Hartree-type equations in one space dimension

We study the higher-order subcritical Hartree-type equations in one space dimension [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text], where [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] the Riesz potential [Formula: see text] is defined by [Formula: see text] where ∗ denotes the convolution in [Formula: see text] Our aim is to find the large time asymptotic behavior of solutions to the Cauchy problem. From the point of view of large time asymptotic behavior of solutions, [Formula: see text] means that the nonlinearity is the subcritical one. Our method cannot be applied to the case [Formula: see text], which is considered as the cubic nonlinearity with a time growth [Formula: see text].