Well-Posedness of a Class of Radial Inhomogeneous Hartree Equations
Well-Posedness of a Class of Radial Inhomogeneous Hartree Equations
The present paper investigates the following inhomogeneous generalized Hartree equation iu˙+Δu=±|u|p−2|x|b(Iα∗|u|p|·|b)u, where the wave function is u:=u(t,x):R×RN→C, with N≥2. In addition, the exponent b>0 gives an unbounded inhomogeneous term |x|b and Iα≈|·|−(N−α) denotes the Riesz-potential for certain 0<α<N. In this work, our aim is to establish the local existence of …