arXiv subjects

Yibin Xiao

Publications and source records attributed to Yibin Xiao.

4 recordsLinked to original sources

arXiv2026

The existence and stability for a class of fuzzy fractional boundary value problems constrained by variational inequalities

In this paper, the existence and stability of a new system consisting of fuzzy fractional differential inclusions (FFDIs) with integral boundary conditions and variational inequalities are considered in Euclidean spaces. This system integrates the features of both FFDIs with integral boundary conditions and fractional differential variational inequalities in a unified framework. The existence of solutions for this system is established under some mild conditions. Moreover, the semicontinuity of the solution map for the perturbed system is investigated with respect to parameter perturbations. Finally, we use two numerical examples to show the validity of the above theoretical findings.

math.OC↗

arXiv2025

Sharp Stability of Solitons for the Cubic-Quintic NLS on R^2

This paper concerns with the cubic-quintic nonlinear Schrödinger equation on R^2. A family of new variational problems related to the solitons are introduced and solved. Some key monotonicity and uniqueness results are obtained. Then the orbital stability of solitons at every frequency are proved in terms of the Cazenave and Lions' argument. And classification of normalized ground states is first presented. Our results settle the questions raised by Lewin and Rota Nodari as well as Carles and Sparber.

math.AP↗

arXiv2025

Uniqueness and stability of normalized ground states for Hartree equation with a harmonic potential

The dynamic properties of normalized ground states for the Hartree equation with a harmonic potential are addressed. The existence of normalized ground state for any prescribed mass is confirmed according to mass-energy constrained variational approach. The uniqueness is shown by the strictly convex properties of the energy functional. Moreover, the orbital stability of every normalized ground state is proven in terms of the Cazenave and Lions' argument.

math.AP↗

arXiv2025

A General Mixed-Order Primal-Dual Dynamical System with Tikhonov Regularization

In a Hilbert space, we propose a class of general mixed-order primal-dual dynamical systems with Tikhonov regularization for a convex optimization problem with linear equality constraints. The proposed dynamical system is characterized by three time-dependent parameters, i.e., general viscous damping, time scaling, and Tikhonov regularization coefficients, which can incorporate as special cases some existing mixed-order primal-dual dynamical systems in the literature. With some appropriate conditions on the parameters, we analyze by constructing suitable Lyapunov functions the asymptotic convergence properties of the proposed dynamical system, where a convergence rate of O(1/(t^2β(t))) for the objective function error and a convergence rate of o(1/β(t)) for the primal-dual gap are established. Moreover, we further prove the strong convergence of the trajectory generated by the proposed dynamical system. Finally, we carry out some numerical experiments to illustrate the obtained theoretical results of the proposed dynamical system.

math.OC↗