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

Abstract

In this paper, we address the mathematical analysis of a nonlinear Schrodinger equation incorporating 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 fixedpoint theory. We prove the existence of solutions using Krasnosel’skii’s theoremandestablish uniqueness via the Banach contraction mapping principle. Wealso investigate Ulam–Hyers stability, confirming the continuous dependence of solutions on initial data. To support the theory, a representative 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.