Here, the Cauchy problem for linear and nonlinear nonlocal Schrödinger equations are studied. The equation involves a convolution integral operators with a general kernel operator functions whose Fourier transform are operator functions defined in a Hilbert space H together with some growth conditions. By assuming enough smoothness on the initial data and the operator functions, the local and global existence and uniqueness of solutions are established. We can obtain a different classes of nonlocal Schr ödinger equations by choosing the space H and linear operators, which occur in a wide variety of physical systems

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非局部抽象薛定谔方程及其应用的柯西问题

在这里，研究了线性和非线性非局部薛定谔方程的柯西问题。该方程涉及一个卷积积分算子和一个通用核算子函数，其傅立叶变换是在希尔伯特空间H 中定义的算子函数以及一些增长条件。通过假设初始数据和算子函数足够平滑，就建立了解的局部和全局存在唯一性。我们可以通过选择空间H和线性算子来获得不同类别的非局部薛定谔方程，它们出现在各种物理系统中