Existence, Uniqueness and Ulam-Hyers stability of solutions for a nonlinear Schrödinger equation with inverse-power potential and mixed type nonlinearities

In this paper, we address the mathematical analysis of a nonlinear Schrödinger equation incor-porating an inverse-power potential alongside mixed power-type and Choquard-type nonlinearities. Such models are relevant in quantum mechanics and nonlinear optics due to their inclusion of singular potentials and long-range nonlocal effects. The equation is transformed using the Duhamel principle into an integral form suitable for fixed-point theory. We prove the existence of solutions using Krasnosel’skii’s theorem and establish uniqueness via the Banach contraction mapping principle. We also investigate Ulam-Hyers stability, confirming the continuous dependence of solutions on initial data. To support the theory, a repre-sentative example is provided, complemented by graphical interpretation. This work contributes a unified treatment of singular and nonlocal interactions, extending existing analytical techniques to more general nonlinear dispersive systems.