@article{article_1754735, title={Optimal Control Problem and Integral Quality Criteria with a Special Gradient Term}, journal={The Eurasia Proceedings of Science Technology Engineering and Mathematics}, volume={34}, pages={310–319}, year={2025}, DOI={10.55549/epstem.1754735}, author={Salmanov, Vugar Ibrahim}, keywords={Schrödinger equation, Optimal control problem, Complex potential}, abstract={The paper deals with the optimal control problem with the full-range integral performance criterion
for the nonlinear Schrödinger equation with the specific gradient summand and the complex potential when the
performance criterion is the full-range integral. Concurrently, the first variation formula of the performance
criterion under consideration and via which the necessary condition is established in the form of a variation
inequality is found. This article investigates the differentiability of the optimal control problem for a threedimensional nonlinear no stationary Schrödinger equation with a special gradient term and a real-valued
potential, when the potential depending on both spatial and time dependence and is sought in the class of
measurable bounded functions, and the coefficient in the nonlinear part of the equation is a complex number.
Therefore, this work differs from previously studied problems nonlinear Schrödinger equation with a specific
gradient term, complex potential and is relevant in its significance and also of scientific interest.}, publisher={ISRES Publishing}