Optimization problems for discrete and diierential inclusions have many important applications and generalize both standard and nonstandard models in optimal control for open-loop and closed-loop control systems. In this paper we consider optimal control problems for dynamic systems governed by such inclusions with general endpoint constraints. We provide a variational analysis of diierential i...

Variational inequality theory has become a rich source of inspiration in the pure and applied mathematics. Variational inequalities not only have stimulated new results dealing with nonlinear partial differential equations, but also have been used in a large variety of problems arising in mechanics, physics, optimization and control nonlinear programming, economics and transportation equilibriu...

We present solutions to the Eshelby conjectures based on a variational inequality. We first discuss the meanings of the original Eshelby’s statement. By Fourier analysis, we establish the connection between the homogeneous Eshelby inclusion problem and the classic Newtonian potential problem. We then proceed to the solutions of the Eshelby conjectures. Under some hypothesis on the material prop...

Correspondence: chwhappy@163. com Department of Science, Nanchang Institute of Technology, Nanchang 330099, P. R. China Abstract In this article, we introduce and study a new system of generalized quasi-variationallike inclusions with noncompact valued mappings. By using the h-proximal mapping technique, we prove the existence of solutions and the convergence of some new N-step iterative algori...

The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by the means of the proximal subdifferential of the no...

We discuss equilibria, dynamics and regularity for Smoluchowski equations coupled to Navier-Stokes equations. Introduction We consider mixtures of fluids and microscopic inclusions. The microscopic inclusions are characterized by state variables m ∈ M , where M is a compact smooth Riemannian manifold without boundary. The simplest example is that of microscopic rods with directors m ∈ S. The mi...

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two variables and linear coupling, our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes. The breadth and flexib...